WEBVTT 00:00:00.000 --> 00:00:01.620 Welcome back to the Deep Dive. This is where 00:00:01.620 --> 00:00:04.059 we take your entire stack of sources, the dense 00:00:04.059 --> 00:00:06.360 articles, the complicated research, your personal 00:00:06.360 --> 00:00:09.259 notes, and synthesize it all into the deep knowledge 00:00:09.259 --> 00:00:11.820 you need, delivered efficiently and engagingly. 00:00:11.820 --> 00:00:14.619 That's right. Today, we are undertaking a deep 00:00:14.619 --> 00:00:18.120 dive into a concept so fundamental, it dictates, 00:00:18.140 --> 00:00:20.960 well, the growth of civilization, the state of 00:00:20.960 --> 00:00:23.219 global trade, and even your personal spending 00:00:23.219 --> 00:00:26.699 habits. It really is the single most pervasive 00:00:26.699 --> 00:00:29.500 price in the entire financial world. And our 00:00:29.500 --> 00:00:31.600 sources today, they really reflect that breadth. 00:00:31.820 --> 00:00:34.359 We're looking at a remarkable historical sweep 00:00:34.359 --> 00:00:37.799 moving from, you know, 5000 year old Sumerian 00:00:37.799 --> 00:00:40.380 documents right up to 21st century theories of 00:00:40.380 --> 00:00:42.700 liquidity. And what's our mission here? Our mission 00:00:42.700 --> 00:00:45.780 is critical to move beyond just calculating interest 00:00:45.780 --> 00:00:48.119 and to truly understand the historical, moral, 00:00:48.179 --> 00:00:52.380 and mathematical underpinnings of why we pay 00:00:52.380 --> 00:00:54.600 or receive the price of money. Okay, let's unpack 00:00:54.600 --> 00:00:56.340 this. We use the word interest constantly, but 00:00:56.340 --> 00:00:57.939 I think it sometimes gets conflated with other 00:00:57.939 --> 00:01:00.340 financial terms. So to start, let's nail down 00:01:00.340 --> 00:01:03.399 the core, pure definition. Fundamentally, interest 00:01:03.399 --> 00:01:06.700 is the cost of borrowing money. It's a payment 00:01:06.700 --> 00:01:10.049 made by a debtor. or a borrower to a lender, 00:01:10.150 --> 00:01:12.810 or sometimes a depositor, of an amount that is 00:01:12.810 --> 00:01:15.370 specifically above the repayment of the principal 00:01:15.370 --> 00:01:18.170 sum. OK, above the original amount. Exactly. 00:01:18.430 --> 00:01:21.269 And crucially, this payment is predetermined 00:01:21.269 --> 00:01:23.750 and paid at a particular rate over a specific 00:01:23.750 --> 00:01:26.430 period. And the roles here can sometimes be confusing. 00:01:26.569 --> 00:01:30.269 If I put, say, $10 ,000 into a savings account, 00:01:30.510 --> 00:01:33.510 who is the lender and who is the borrower? That's 00:01:33.510 --> 00:01:34.989 a great question because it feels backwards. 00:01:35.349 --> 00:01:37.890 In that case, you, the customer, are the lender. 00:01:38.010 --> 00:01:40.030 You are supplying the bank with your capital. 00:01:40.250 --> 00:01:42.609 So the bank is the borrower. The bank is the 00:01:42.609 --> 00:01:45.239 borrower. They pay you interest for the use of 00:01:45.239 --> 00:01:47.439 your money, which they then, of course, lend 00:01:47.439 --> 00:01:49.760 out at a higher rate. The interest rate itself 00:01:49.760 --> 00:01:52.099 is merely the amount paid or received over that 00:01:52.099 --> 00:01:54.540 period divided by the principal sum, and it's 00:01:54.540 --> 00:01:57.140 usually expressed as an annual percentage. We 00:01:57.140 --> 00:01:59.640 absolutely must distinguish this from other common 00:01:59.640 --> 00:02:02.640 financial terms. Otherwise, you know, the accounting 00:02:02.640 --> 00:02:05.519 gets messy. For example, interest versus a fee. 00:02:05.719 --> 00:02:08.560 Yes, a crucial distinction. Interest is entirely 00:02:08.560 --> 00:02:10.960 dependent on the principal amount, the rate, 00:02:11.099 --> 00:02:14.560 and the time the money is used. A fee, by contrast, 00:02:14.840 --> 00:02:17.539 is a fixed charge. It's paid to a lender or a 00:02:17.539 --> 00:02:21.460 third party, usually for processing, administering, 00:02:21.460 --> 00:02:24.340 or underwriting the loan. So like a loan origination 00:02:24.340 --> 00:02:27.219 fee. Exactly. A loan officer's fixed commission 00:02:27.219 --> 00:02:30.300 is a fee. The 7 % annual charge on the remaining 00:02:30.300 --> 00:02:32.479 balance is the interest. And what about equity? 00:02:32.680 --> 00:02:35.400 If I invest in a successful company and I get 00:02:35.400 --> 00:02:38.340 a quarterly payout, that's a dividend. Why is 00:02:38.340 --> 00:02:40.819 that not considered interest? Because the nature 00:02:40.819 --> 00:02:43.319 of the relationship is entirely different. Interest 00:02:43.319 --> 00:02:46.370 is received by a lender based on a contractual 00:02:46.370 --> 00:02:49.830 preset rate. A dividend is received by a shareholder 00:02:49.830 --> 00:02:52.550 who is, by definition, an owner of the company. 00:02:52.729 --> 00:02:55.669 As an owner, you assume risk. Ah, so there's 00:02:55.669 --> 00:02:58.069 risk involved. A huge amount of risk. The dividend 00:02:58.069 --> 00:03:00.490 is paid out of the company's actual profits and 00:03:00.490 --> 00:03:02.789 its amount is determined after the fact based 00:03:02.789 --> 00:03:05.430 on how well the company performed. It's a pro 00:03:05.430 --> 00:03:07.469 -rata share and the reward for that risk taking. 00:03:07.669 --> 00:03:11.030 So the core distinction is interest is fixed 00:03:11.030 --> 00:03:14.599 and contractual. paid to a lender. A profit or 00:03:14.599 --> 00:03:17.539 a dividend is variable and it's paid to an owner 00:03:17.539 --> 00:03:20.340 or an investor who shared in the actual risk. 00:03:20.479 --> 00:03:22.860 Exactly. It separates the idea of lending capital 00:03:22.860 --> 00:03:26.199 from the idea of risking capital. And once we 00:03:26.199 --> 00:03:28.860 understand interest as the price of time and 00:03:28.860 --> 00:03:31.780 capital, we have to immediately discuss the dynamic 00:03:31.780 --> 00:03:35.560 engine that drives that price. Compounding. Here's 00:03:35.560 --> 00:03:37.699 where it gets really interesting. Compound interest, 00:03:37.979 --> 00:03:40.620 which Albert Einstein may or may not have called 00:03:40.620 --> 00:03:42.900 the eighth wonder of the world. Right. That's 00:03:42.900 --> 00:03:45.439 probably apocryphal. Probably. But it's a great 00:03:45.439 --> 00:03:47.580 line. It's the idea that you earn interest not 00:03:47.580 --> 00:03:49.740 only on the original principle, but also on all 00:03:49.740 --> 00:03:51.439 the interest that is already accumulated. It 00:03:51.439 --> 00:03:53.879 creates exponential growth. If your savings account 00:03:53.879 --> 00:03:56.520 compounds quarterly, the second quarter's interest 00:03:56.520 --> 00:03:58.460 is calculated on a slightly larger principle 00:03:58.460 --> 00:04:01.080 than the first. It just it snowballs the growth. 00:04:01.240 --> 00:04:03.199 And it works the other way, too, with debt. Oh, 00:04:03.240 --> 00:04:06.039 absolutely. On the debt side, if you miss a credit 00:04:06.039 --> 00:04:08.580 card payment, the interest from that missed month 00:04:08.580 --> 00:04:10.900 is immediately added to your principal and your 00:04:10.900 --> 00:04:13.180 next interest charge will be calculated on that 00:04:13.180 --> 00:04:15.759 larger inflated amount. And this exponential 00:04:15.759 --> 00:04:18.720 nature of compounding is so central to our understanding 00:04:18.720 --> 00:04:22.300 of finance that, as you noted, its mathematical 00:04:22.300 --> 00:04:24.779 study led to the discovery of the fundamental 00:04:24.779 --> 00:04:27.800 constant E. Yes, we are absolutely going to dive 00:04:27.800 --> 00:04:30.720 into that deep math later. But first, let's establish 00:04:30.720 --> 00:04:33.019 the context, because the story of interest is, 00:04:33.060 --> 00:04:35.300 I mean, it's older than democracy. Is it really? 00:04:35.480 --> 00:04:37.899 Oh, yeah. And it's a story rooted in surprising 00:04:37.899 --> 00:04:40.699 necessity. The sources make it clear that credit 00:04:40.699 --> 00:04:43.480 the ability to loan and borrow predates coinage 00:04:43.480 --> 00:04:46.810 by millennia. Millennia. The first concrete written 00:04:46.810 --> 00:04:49.610 evidence of systematic credit comes from Sumerian 00:04:49.610 --> 00:04:52.790 documents, specifically cuneiform tablets, dating 00:04:52.790 --> 00:04:56.829 back to 3000 BC in Mesopotamia. 3000 BC. That 00:04:56.829 --> 00:04:58.589 is staggering. What were they loaning? I mean, 00:04:58.610 --> 00:05:01.290 it wasn't cash. No, the loans were primarily 00:05:01.290 --> 00:05:04.709 in grain. the agricultural staple in silver, 00:05:04.910 --> 00:05:07.610 which served as the standardized metal. And what's 00:05:07.610 --> 00:05:10.529 crucial is that these were systematic, institutionalized 00:05:10.529 --> 00:05:13.629 loans used to manage the cyclical nature of agriculture. 00:05:14.089 --> 00:05:16.569 A farmer might need grain for planting season, 00:05:16.769 --> 00:05:18.850 and they'd promise repayment after the harvest. 00:05:19.170 --> 00:05:21.930 So what was the early justification for charting 00:05:21.930 --> 00:05:24.949 interest on a bag of seeds or a piece of silver? 00:05:25.089 --> 00:05:27.709 The theory likely arose from the most practical 00:05:27.709 --> 00:05:31.490 observation. productivity. If you loan a shepherd 00:05:31.490 --> 00:05:34.350 10 sheep, those sheep will reproduce. If you 00:05:34.350 --> 00:05:36.850 loan a farmer 10 measures of grain, those seeds 00:05:36.850 --> 00:05:39.170 will multiply in the field. So the lender felt 00:05:39.170 --> 00:05:41.750 they deserved a cut of that natural growth. Exactly. 00:05:42.110 --> 00:05:44.689 The lender argued, quite reasonably, that they 00:05:44.689 --> 00:05:46.370 deserved a share of that natural multiplication, 00:05:46.750 --> 00:05:49.209 arguing the acquired goods could multiply themselves. 00:05:49.649 --> 00:05:52.069 This established the idea of a natural yield 00:05:52.069 --> 00:05:54.990 or interest. That makes perfect sense for productive 00:05:54.990 --> 00:05:57.529 assets like livestock, which literally reproduce. 00:05:57.970 --> 00:06:00.629 But what happens when that same rate, the sources 00:06:00.629 --> 00:06:03.550 say it was around 20 % annually, is applied to 00:06:03.550 --> 00:06:05.589 something that doesn't reproduce, like silver. 00:06:05.750 --> 00:06:08.410 And that is precisely where the philosophical 00:06:08.410 --> 00:06:11.310 tension and moral objections began, almost immediately. 00:06:11.870 --> 00:06:14.269 The first written evidence we have of compound 00:06:14.269 --> 00:06:17.970 interest dates to roughly 2400 B .C., where that 00:06:17.970 --> 00:06:20.490 standard annual interest rate of about 20 percent 00:06:20.490 --> 00:06:23.769 was codified and it was often applied to both 00:06:23.769 --> 00:06:26.850 grain and silver. And while that system was obviously 00:06:26.850 --> 00:06:29.209 essential for urbanization and managing harvests. 00:06:29.290 --> 00:06:31.569 It was. The fairness of charging 20 percent on 00:06:31.569 --> 00:06:33.790 what they called sterile silver money that doesn't 00:06:33.790 --> 00:06:36.660 inherently grow. That became a massive point 00:06:36.660 --> 00:06:39.040 of contention. Huge. And this contention leads 00:06:39.040 --> 00:06:41.660 us directly into the concept of usury, which 00:06:41.660 --> 00:06:43.939 for most of history didn't just mean excessive 00:06:43.939 --> 00:06:46.639 interest, but often any interest at all, especially 00:06:46.639 --> 00:06:48.819 when you were lending to a co -religionist. That's 00:06:48.819 --> 00:06:51.420 right. The strong moral and religious prohibitions 00:06:51.420 --> 00:06:53.899 appeared very early. They did. For instance, 00:06:54.079 --> 00:06:56.240 in the ancient Jewish faith, there were prohibitions 00:06:56.240 --> 00:06:59.079 against charging neshek or usury to other Jews. 00:06:59.420 --> 00:07:02.360 This reflected a necessity -based tribal view 00:07:02.360 --> 00:07:04.939 where lending money to a neighbor, well, it should 00:07:04.939 --> 00:07:07.439 be an act of charity, not a commercial transaction 00:07:07.439 --> 00:07:10.019 designed to profit from that neighbor's misfortune. 00:07:10.240 --> 00:07:13.959 And that prohibition was powerfully adopted and 00:07:13.959 --> 00:07:16.100 then expanded by early Christianity during the 00:07:16.100 --> 00:07:19.089 Roman Empire. Dramatically so. The First Council 00:07:19.089 --> 00:07:22.910 of Nicaea in 325 AD strictly forbade clergy from 00:07:22.910 --> 00:07:25.449 practicing usury, and they defined it as lending 00:07:25.449 --> 00:07:28.730 above 1 % per month. Which works out to, what, 00:07:28.769 --> 00:07:32.750 about 12 .7 % a year? Roughly, yes. And later, 00:07:32.889 --> 00:07:35.569 the moral condemnation expanded to the laity, 00:07:35.709 --> 00:07:38.050 culminating in the powerful arguments of St. 00:07:38.069 --> 00:07:40.709 Thomas Aquinas in the 13th century. What was 00:07:40.709 --> 00:07:43.589 Aquinas' specific theological argument against 00:07:43.589 --> 00:07:46.439 charging interest? He argued it was intrinsically 00:07:46.439 --> 00:07:48.819 wrong because it constituted double charging. 00:07:49.300 --> 00:07:51.680 He used Aristotle's definition that money is 00:07:51.680 --> 00:07:53.759 sterile. It's just a medium of exchange, not 00:07:53.759 --> 00:07:55.699 a productive asset like a farm or a workshop. 00:07:56.000 --> 00:07:58.259 OK, so how is it double charging? By charging 00:07:58.259 --> 00:08:00.540 interest, you are effectively selling the buyer 00:08:00.540 --> 00:08:02.939 the principal sum and then charging them separately 00:08:02.939 --> 00:08:05.680 for the use of that sum. But since the use and 00:08:05.680 --> 00:08:07.800 the principal are inseparable when you're dealing 00:08:07.800 --> 00:08:09.600 with sterile money, you're basically selling 00:08:09.600 --> 00:08:12.360 the same thing twice. That really reflects the 00:08:12.360 --> 00:08:14.600 economic reality of the time, doesn't it? If 00:08:14.600 --> 00:08:16.800 you needed a loan in the medieval period, it 00:08:16.800 --> 00:08:18.879 was almost always a tragedy. Your house burned 00:08:18.879 --> 00:08:21.560 down, your sheep died. It was a loan of necessity 00:08:21.560 --> 00:08:24.379 for consumption. Exactly. It wasn't a productive 00:08:24.379 --> 00:08:26.199 investment that would yield a profit for the 00:08:26.199 --> 00:08:29.019 borrower. So the moral reproach was based on 00:08:29.019 --> 00:08:31.300 the fact that the lender was profiting from someone 00:08:31.300 --> 00:08:34.259 else's necessity and distress, and the money 00:08:34.259 --> 00:08:36.620 itself wasn't creating any new goods or services. 00:08:36.960 --> 00:08:39.600 There was no productive value. None at all, in 00:08:39.600 --> 00:08:42.799 their view. So if the moral framework was so 00:08:42.799 --> 00:08:45.970 rigid, How did the West eventually transition 00:08:45.970 --> 00:08:48.870 to a world where charging interest is, I mean, 00:08:48.889 --> 00:08:50.929 it's just standard practice? The catalyst was 00:08:50.929 --> 00:08:53.330 the Renaissance. It was the explosion of commerce, 00:08:53.370 --> 00:08:56.809 of trade, of mobility. Money stopped being primarily 00:08:56.809 --> 00:08:58.990 a cushion against poverty and started becoming 00:08:58.990 --> 00:09:01.409 a tool of production. Ah, so when borrowed money 00:09:01.409 --> 00:09:05.210 was used to finance a new voyage or equip a printing 00:09:05.210 --> 00:09:08.289 press. Or start a new business activities that 00:09:08.289 --> 00:09:11.289 generated significant wealth. The moral perception 00:09:11.289 --> 00:09:14.370 shifted entirely. The interest became compensation 00:09:14.370 --> 00:09:17.350 for the lender's opportunity cost and the risk 00:09:17.350 --> 00:09:19.730 of the new enterprise rather than just profiting 00:09:19.730 --> 00:09:21.909 from distress. The philosophical justification 00:09:21.909 --> 00:09:25.070 changed from the lender profits from my need 00:09:25.070 --> 00:09:28.509 to something like the lender deserves compensation 00:09:28.509 --> 00:09:31.289 because their money enabled my profit. That's 00:09:31.289 --> 00:09:33.750 the intellectual jump that eventually legalized 00:09:33.750 --> 00:09:36.509 and normalized interest across the secular economies 00:09:36.509 --> 00:09:39.929 of Europe. However, that moral objection, RIBA, 00:09:40.070 --> 00:09:42.850 it remains central to Islamic finance today. 00:09:42.970 --> 00:09:45.389 Let's look at that framework because it's a powerful 00:09:45.389 --> 00:09:48.149 modern example of how to run a complex financial 00:09:48.149 --> 00:09:50.730 system without the mechanism of predetermined 00:09:50.730 --> 00:09:53.049 interest. The modern Islamic banking movement 00:09:53.049 --> 00:09:55.450 grew significantly in the later 20th century, 00:09:55.610 --> 00:09:58.450 and the central prohibition remains. Making money 00:09:58.450 --> 00:10:00.809 out of money is unacceptable. Predetermined loan 00:10:00.809 --> 00:10:03.830 repayment or REBA is prohibited. This means a 00:10:03.830 --> 00:10:05.649 standard loan contract with a fixed interest 00:10:05.649 --> 00:10:08.049 rate is impossible. So if a bank can't charge 00:10:08.049 --> 00:10:09.870 a fixed rate, how does a financial institution 00:10:09.870 --> 00:10:13.049 profit and how do savers get a return? They share 00:10:13.049 --> 00:10:16.070 the risk. The financial institution acts as a 00:10:16.070 --> 00:10:19.169 partner, not a lender. This is achieved through 00:10:19.169 --> 00:10:22.419 profit loss sharing schemes. For instance, instead 00:10:22.419 --> 00:10:24.399 of lending you money to buy a house and charging 00:10:24.399 --> 00:10:27.700 6 % interest, the bank might enter a joint venture, 00:10:27.860 --> 00:10:31.279 a musharaka, or a cost -plus -profit contract, 00:10:31.620 --> 00:10:35.100 a murabaha, to finance the purchase. Can you 00:10:35.100 --> 00:10:37.220 give us a specific example of how that might 00:10:37.220 --> 00:10:39.940 work? Sure. Let's say you're purchasing a piece 00:10:39.940 --> 00:10:42.480 of equipment for a business. Under an Islamic 00:10:42.480 --> 00:10:45.120 banking model, the bank might purchase the equipment 00:10:45.120 --> 00:10:47.480 outright and then lease it to the business for 00:10:47.480 --> 00:10:50.169 a fixed agreed -upon period. The lease payments 00:10:50.169 --> 00:10:52.850 would be determined by the asset's use and depreciation, 00:10:52.970 --> 00:10:55.490 not a floating interest rate. Or they could become 00:10:55.490 --> 00:10:58.169 partners. Or, more commonly, they act as partners, 00:10:58.289 --> 00:11:00.830 mudarba, investing capital and sharing the eventual 00:11:00.830 --> 00:11:03.629 profits according to a pre -agreed ratio. But, 00:11:03.750 --> 00:11:05.970 and this is key, they also share in any eventual 00:11:05.970 --> 00:11:08.169 losses. What's fascinating is that this requires 00:11:08.169 --> 00:11:11.190 all transactions to be asset -backed. They can't 00:11:11.190 --> 00:11:14.250 just lend cash against nothing. Precisely. The 00:11:14.250 --> 00:11:16.669 money has to be tied to a real -world productive 00:11:16.669 --> 00:11:20.590 asset or enterprise. This inherently forces financial 00:11:20.590 --> 00:11:23.009 institutions to focus on the productivity of 00:11:23.009 --> 00:11:25.950 the economy, the very justification that helped 00:11:25.950 --> 00:11:29.169 lift the usury ban in the West, but without reverting 00:11:29.169 --> 00:11:32.230 to a predetermined contract rate. It emphasizes 00:11:32.230 --> 00:11:35.090 that money must be used to create wealth, not 00:11:35.090 --> 00:11:37.629 just be extracted from debt. That provides an 00:11:37.629 --> 00:11:40.009 incredible transition. If the philosophical justification 00:11:40.009 --> 00:11:43.269 hinges on productivity, then the mechanical growth 00:11:43.269 --> 00:11:45.210 of that productive wealth is what we need to 00:11:45.210 --> 00:11:47.990 focus on next, the mathematics of interest. Right. 00:11:48.110 --> 00:11:50.889 Let's move from philosophy to pure math, starting 00:11:50.889 --> 00:11:52.909 with the distinction between simple and compound 00:11:52.909 --> 00:11:55.830 interest. Simple interest is what we first look 00:11:55.830 --> 00:11:58.029 at in school, and it's calculated only on the 00:11:58.029 --> 00:12:00.309 original principal amount, completely excluding 00:12:00.309 --> 00:12:02.879 any compounding effect. Okay, so if a listener 00:12:02.879 --> 00:12:05.220 has a loan or credit card that charges, say, 00:12:05.299 --> 00:12:08.759 12 .99 % annually, let's walk through how simple 00:12:08.759 --> 00:12:11.799 interest would be calculated on a $2 ,500 balance. 00:12:12.200 --> 00:12:17.860 Okay. If that 12 .99 % annual rate, or .1299, 00:12:18.080 --> 00:12:21.679 is applied over one month, and we assume 12 payment 00:12:21.679 --> 00:12:24.240 periods in a year, you just calculate the simple 00:12:24.240 --> 00:12:26.419 interest for that month. It's the annual rate 00:12:26.419 --> 00:12:29.129 times the principal. Divided by the number of 00:12:29.129 --> 00:12:33.350 periods. So that's 0 .1299 times 2 ,500 divided 00:12:33.350 --> 00:12:37.429 by 12. Which comes out to approximately $27 .06. 00:12:37.649 --> 00:12:40.309 So if the borrower paid exactly that amount, 00:12:40.509 --> 00:12:43.090 their principal remains at 2 ,500. And if they 00:12:43.090 --> 00:12:45.809 did this for three months, the total simple interest 00:12:45.809 --> 00:12:47.669 would be just three times that amount, so about 00:12:47.669 --> 00:12:51.009 $81. The calculation stays flat? It stays completely 00:12:51.009 --> 00:12:53.549 flat, exactly. It ignores any interest that might 00:12:53.549 --> 00:12:55.950 have accrued. That sounds wonderfully manageable. 00:12:56.600 --> 00:12:58.740 But as we know, the real world is almost entirely 00:12:58.740 --> 00:13:01.159 dominated by compound interest, which is where 00:13:01.159 --> 00:13:03.860 things become exponential and, well, potentially 00:13:03.860 --> 00:13:06.360 far more punitive if you're borrowing. Compound 00:13:06.360 --> 00:13:08.419 interest is what happens when the interest earned 00:13:08.419 --> 00:13:10.840 or charged is added back to the principal, and 00:13:10.840 --> 00:13:12.980 subsequent interest calculations are based on 00:13:12.980 --> 00:13:15.399 that newly inflated balance. The frequency of 00:13:15.399 --> 00:13:18.200 compounding daily, monthly, semi -annually is 00:13:18.200 --> 00:13:19.879 what determines the effective rate of growth. 00:13:20.100 --> 00:13:22.279 Let's use a quick comparison to show the impact 00:13:22.279 --> 00:13:25.950 of that compounding frequency. Imagine two investments, 00:13:26.190 --> 00:13:29.710 both with a 6 % simple annual rate. One is an 00:13:29.710 --> 00:13:32.730 annual CD. It pays 6 % once a year. The other 00:13:32.730 --> 00:13:35.710 is a bond that pays 6 % semi -annually so, 3 00:13:35.710 --> 00:13:39.539 % every six months. Okay. On a $10 ,000 investment, 00:13:39.860 --> 00:13:43.019 the annual CD simply pays you $600 at the end 00:13:43.019 --> 00:13:45.860 of the year. The semiannual bond, however, pays 00:13:45.860 --> 00:13:48.940 $300 after the first six months. This is the 00:13:48.940 --> 00:13:51.360 crucial moment for the compounding effect. Because 00:13:51.360 --> 00:13:53.320 the bondholder can immediately reinvest that 00:13:53.320 --> 00:13:57.059 $300. Yes. They now have a principle of $10 ,300 00:13:57.059 --> 00:13:59.840 for the next six months. So when the second coupon 00:13:59.840 --> 00:14:02.580 is paid, it's 3 % of that larger amount, which 00:14:02.580 --> 00:14:05.799 is $309. So over the full year, the investor 00:14:05.799 --> 00:14:09.899 has earned $300 plus $309 for a total of $609. 00:14:10.320 --> 00:14:12.779 Right. So even though the stated rate was 6%, 00:14:12.779 --> 00:14:15.659 the investor's effective annual rate, the AER, 00:14:15.840 --> 00:14:19.799 is actually 6 .09%. That extra $9 is the direct 00:14:19.799 --> 00:14:21.980 result of the compounding frequency. And this 00:14:21.980 --> 00:14:23.879 leads us to the formal mathematical expression 00:14:23.879 --> 00:14:26.460 for that annual equivalent rate. It does. It's 00:14:26.460 --> 00:14:29.100 1 plus r divided by n, all raised to the power 00:14:29.100 --> 00:14:32.639 of n minus 1, where r is the nominal annual rate 00:14:32.639 --> 00:14:35.600 and n is the number of compounding periods per 00:14:35.600 --> 00:14:39.159 year. In our bond example, that's 1 plus 0 .06 00:14:39.159 --> 00:14:44.200 over 2 squared minus 1, which gives you 6 .09%. 00:14:44.200 --> 00:14:47.279 This simple realization... that increasing the 00:14:47.279 --> 00:14:49.259 frequency of compounding increases the rate of 00:14:49.259 --> 00:14:52.039 return is what led jacob bernoulli to his profound 00:14:52.039 --> 00:14:54.600 discovery of the constant e this is a perfect 00:14:54.600 --> 00:14:57.399 example of how finance drives pure mathematics 00:14:57.399 --> 00:15:00.840 it truly is an aha moment in history bernoulli 00:15:00.840 --> 00:15:03.919 back in 1683 was pondering what happens if you 00:15:03.919 --> 00:15:06.000 take that compounding process to its logical 00:15:06.000 --> 00:15:08.840 extreme he devised a thought experiment Start 00:15:08.840 --> 00:15:11.700 with $1 and offer a 100 % annual rate. Okay, 00:15:11.779 --> 00:15:13.779 so compounding annually gives you $2. Right. 00:15:13.860 --> 00:15:16.559 Compounding semi -annually yields $1 times 1 00:15:16.559 --> 00:15:20.980 .5 times 1 .5 again, so $2 .25. If you compound 00:15:20.980 --> 00:15:24.460 monthly, the return jumps to about $2 .61. Bernoulli 00:15:24.460 --> 00:15:26.480 wondered, what happens if we compound infinitely 00:15:26.480 --> 00:15:29.340 often? Every second, every nanosecond, does the 00:15:29.340 --> 00:15:31.340 result become infinite? You would intuitively 00:15:31.340 --> 00:15:33.480 think that, yeah, if you divide the interest 00:15:33.480 --> 00:15:35.879 rate by an infinite number of periods, you get 00:15:35.879 --> 00:15:38.750 an infinitely growing return. But Bernoulli proved 00:15:38.750 --> 00:15:41.250 that it doesn't. As you increase the frequency 00:15:41.250 --> 00:15:44.570 of compounding n toward infinity, the calculation 00:15:44.570 --> 00:15:47.929 approaches a finite fixed limit. Why is that? 00:15:48.129 --> 00:15:50.710 Because the increase in frequency is offset by 00:15:50.710 --> 00:15:53.149 the corresponding infinitely small division of 00:15:53.149 --> 00:15:55.470 the rate. The gain from the frequency increase 00:15:55.470 --> 00:15:58.970 is exactly balanced by the rate dilution. Wow. 00:15:59.070 --> 00:16:02.090 Precisely. And that specific finite limit... 00:16:02.269 --> 00:16:05.110 where continuous compounding occurs, is the mathematical 00:16:05.110 --> 00:16:09.669 constant E, approximately 2 .71828. It is the 00:16:09.669 --> 00:16:12.950 limit as n approaches infinity of 1 plus 1n to 00:16:12.950 --> 00:16:15.590 the power of n. That's amazing. The drive to 00:16:15.590 --> 00:16:17.590 understand the best way to earn interest led 00:16:17.590 --> 00:16:19.730 to the discovery of one of nature's most fundamental 00:16:19.730 --> 00:16:22.340 numbers. And it now governs everything from population 00:16:22.340 --> 00:16:25.120 dynamics to pricing complex financial derivatives 00:16:25.120 --> 00:16:27.539 today, which rely on the concept of continuous 00:16:27.539 --> 00:16:30.080 compounding. Now, moving from the purely theoretical 00:16:30.080 --> 00:16:32.519 math to the practical back of the envelope math, 00:16:32.759 --> 00:16:34.659 we need to share some rules of thumb for the 00:16:34.659 --> 00:16:36.759 listener. The first is the famous rule of 72. 00:16:37.279 --> 00:16:39.980 The rule of 72 is perhaps the most useful piece 00:16:39.980 --> 00:16:42.100 of financial shorthand for approximating how 00:16:42.100 --> 00:16:44.120 long it takes for an investment or a debt to 00:16:44.120 --> 00:16:46.559 double. You just take the number 72 and divide 00:16:46.559 --> 00:16:48.799 it by the annual percentage interest rate. So 00:16:48.799 --> 00:16:51.039 if you manage to find an investment yielding 00:16:51.039 --> 00:16:55.379 a steady 6 % annual return. 72 divided by 6 is 00:16:55.379 --> 00:16:58.440 12. It takes approximately 12 years for your 00:16:58.440 --> 00:17:00.899 principal to double. This is enormously useful 00:17:00.899 --> 00:17:02.860 for retirement planning. And on the flip side. 00:17:02.960 --> 00:17:05.119 On the flip side, if you are struggling with 00:17:05.119 --> 00:17:08.059 a high interest credit card at 18%, 72 divided 00:17:08.059 --> 00:17:10.880 by 18 means that debt principal will double in 00:17:10.880 --> 00:17:13.200 only four years, assuming you pay nothing down. 00:17:13.640 --> 00:17:15.579 Our sources know that this rule works incredibly 00:17:15.579 --> 00:17:18.440 well for interest rates up to about 10%. But 00:17:18.440 --> 00:17:20.319 what about outside that range? It's still a very 00:17:20.319 --> 00:17:22.740 good approximation. For a very low rate, say 00:17:22.740 --> 00:17:26.779 4%, the rule of 72 suggests 18 years, while the 00:17:26.779 --> 00:17:30.240 actual doubling time is closer to 17 .7. For 00:17:30.240 --> 00:17:33.380 a very high rate, like 36%, the rule suggests 00:17:33.380 --> 00:17:36.240 two years, but the actual time is closer to 2 00:17:36.240 --> 00:17:39.559 .25. It's an easy rule to memorize, and the error 00:17:39.559 --> 00:17:41.500 is generally small enough to be useful for quick 00:17:41.500 --> 00:17:44.539 decisions. Rule 72 is helpful for the future, 00:17:44.680 --> 00:17:47.119 but we have to issue a serious warning about 00:17:47.119 --> 00:17:49.839 a historical rule of thumb that actively punished 00:17:49.839 --> 00:17:54.140 borrowers, the Rule of 78s. This is a truly dark 00:17:54.140 --> 00:17:56.920 and frankly exploitative chapter in consumer 00:17:56.920 --> 00:18:00.160 finance history. The rule of 78s, also called 00:18:00.160 --> 00:18:03.039 the sum of digits method, was used widely for 00:18:03.039 --> 00:18:05.240 calculating interest allocation on flat rate 00:18:05.240 --> 00:18:07.660 consumer loans in the U .S. and Canada before 00:18:07.660 --> 00:18:10.400 computational power became ubiquitous. The name 00:18:10.400 --> 00:18:12.160 comes from the fact that the sum of the integers 00:18:12.160 --> 00:18:15.559 from 1 to 12 is 78, reflecting a one year loan. 00:18:16.019 --> 00:18:18.519 How was this method used to disadvantage the 00:18:18.519 --> 00:18:20.980 borrower? Well, first, the total interest due 00:18:20.980 --> 00:18:22.960 over the entire life of the loan was calculated 00:18:22.960 --> 00:18:26.019 up front. Then, that interest was allocated using 00:18:26.019 --> 00:18:28.779 a weighted system, but in reverse. For a one 00:18:28.779 --> 00:18:32.339 -year loan, the lender deemed 1 ,278 of all the 00:18:32.339 --> 00:18:35.140 interest to be due in the first month, 1 ,178 00:18:35.140 --> 00:18:37.779 since the second, and so on until the last month 00:18:37.779 --> 00:18:40.420 where only 1 ,178 was allocated. So the interest 00:18:40.420 --> 00:18:42.440 payments were severely front -loaded. You might 00:18:42.440 --> 00:18:44.519 pay the same dollar amount every month, but the 00:18:44.519 --> 00:18:46.140 allocation meant you were paying off the interest 00:18:46.140 --> 00:18:49.519 component first. Precisely. For a borrower, the 00:18:49.519 --> 00:18:52.380 practical effect was brutal. For a one -year 00:18:52.380 --> 00:18:56.019 loan, approximately three -quarters, or 75%, 00:18:56.019 --> 00:18:59.400 of the total interest owed was collected by the 00:18:59.400 --> 00:19:01.599 lender within the first six months. So if you 00:19:01.599 --> 00:19:03.180 came into some money and wanted to pay off your 00:19:03.180 --> 00:19:05.400 loan early. You'd be shocked to find you were 00:19:05.400 --> 00:19:08.019 entitled to almost no refund on interest, having 00:19:08.019 --> 00:19:10.640 already paid the vast majority of it. It effectively 00:19:10.640 --> 00:19:13.660 made early payoff financially punishing, trapping 00:19:13.660 --> 00:19:15.839 borrowers into paying interest for the full term. 00:19:15.960 --> 00:19:18.140 That's predatory. It was recognized as such. 00:19:18.779 --> 00:19:21.819 Thankfully, legislative action was taken. The 00:19:21.819 --> 00:19:24.160 U .S. outlawed the Rule of 78s for mortgages 00:19:24.160 --> 00:19:26.519 and other long -term consumer loans, specifically 00:19:26.519 --> 00:19:30.289 those over five years, starting in 1992. It's 00:19:30.289 --> 00:19:32.589 a stark reminder that the methodology of calculation 00:19:32.589 --> 00:19:35.289 is just as important as the stated rate. One 00:19:35.289 --> 00:19:38.069 final quick note on calculation. How do instruments 00:19:38.069 --> 00:19:40.750 like T -bills or treasury bills calculate interest? 00:19:40.930 --> 00:19:43.109 They're different, right? They are. T -bills 00:19:43.109 --> 00:19:45.769 are known as discount instruments and use a specialized 00:19:45.769 --> 00:19:49.250 method. They don't pay periodic interest payments. 00:19:50.089 --> 00:19:52.890 Instead, the interest is calculated based on 00:19:52.890 --> 00:19:55.069 the difference between the face value and the 00:19:55.069 --> 00:19:57.619 price you paid when you bought it. So if a $1 00:19:57.619 --> 00:20:01.900 ,000 T -bill is sold for $980, the $20 difference 00:20:01.900 --> 00:20:04.400 is the interest you earn when the government 00:20:04.400 --> 00:20:06.380 pays you the full $1 ,000 at maturity. Correct. 00:20:06.480 --> 00:20:09.259 The buyer is discounting the future value to 00:20:09.259 --> 00:20:11.940 arrive at the current purchase price. And that 00:20:11.940 --> 00:20:14.519 interest is prorated using a simple interest 00:20:14.519 --> 00:20:16.819 calculation based on the number of days until 00:20:16.819 --> 00:20:19.740 maturity. It's an inverted calculation method, 00:20:19.880 --> 00:20:22.460 but the principle remains the same. Okay. With 00:20:22.460 --> 00:20:24.500 the history and the math covered, we now shift 00:20:24.500 --> 00:20:27.880 our focus to the macro view. How are these rates 00:20:27.880 --> 00:20:30.380 determined in the actual market? Economically 00:20:30.380 --> 00:20:32.559 speaking, interest is the price of credit. And 00:20:32.559 --> 00:20:35.160 like any price in a market economy, it's driven 00:20:35.160 --> 00:20:37.500 by the scarcity of the commodity, in this case, 00:20:37.500 --> 00:20:39.960 loanable funds, and the intersection of supply 00:20:39.960 --> 00:20:42.880 and demand. The fundamental reason interest rates 00:20:42.880 --> 00:20:45.119 are generally above zero is that loanable funds 00:20:45.119 --> 00:20:47.119 are scarce and there's always competing demand 00:20:47.119 --> 00:20:49.440 for them. But the price of credit isn't uniform. 00:20:50.119 --> 00:20:53.400 I mean, a bank might offer 0 .1 % on a savings 00:20:53.400 --> 00:20:56.400 account, charge 5 % on a mortgage, and demand 00:20:56.400 --> 00:21:00.339 25 % on a credit card. Why the massive variation? 00:21:00.759 --> 00:21:03.339 Because the nominal rate that the borrower sees 00:21:03.339 --> 00:21:06.539 is a compound of several distinct factors. We 00:21:06.539 --> 00:21:08.819 can break the nominal rate down into four essential 00:21:08.819 --> 00:21:11.529 components. The first is the real rate. which 00:21:11.529 --> 00:21:13.970 you can think of as opportunity costs and deferred 00:21:13.970 --> 00:21:16.130 consumption. This compensates the lender for 00:21:16.130 --> 00:21:17.750 giving up the use of their money now. Exactly. 00:21:17.869 --> 00:21:20.609 The lender is deferring consumption. They need 00:21:20.609 --> 00:21:22.690 to be compensated not just for the delay, but 00:21:22.690 --> 00:21:24.470 also for the foregone return they could have 00:21:24.470 --> 00:21:26.509 achieved by investing in the next best alternative. 00:21:27.130 --> 00:21:29.910 If a 1 % risk -free return is possible elsewhere, 00:21:30.230 --> 00:21:33.210 the real rate has to be at least 1%. The second 00:21:33.210 --> 00:21:35.009 factor, and the one that feels most immediate 00:21:35.009 --> 00:21:38.170 to consumers, is inflation. Right. Since we're 00:21:38.170 --> 00:21:40.230 dealing with time and loans often span years 00:21:40.230 --> 00:21:43.109 or decades, the lender faces the risk that future 00:21:43.109 --> 00:21:45.849 dollars will buy less than current dollars. If 00:21:45.849 --> 00:21:48.369 inflation is 3 % and they charge 3 % interest, 00:21:48.630 --> 00:21:50.890 they are simply preserving their purchasing power, 00:21:50.990 --> 00:21:53.450 not making a profit. So how does the market typically 00:21:53.450 --> 00:21:56.309 handle the uncertainty of future inflation? Three 00:21:56.309 --> 00:21:59.599 main ways. Some governments issue real return 00:21:59.599 --> 00:22:02.880 or inflation index bonds where the principal 00:22:02.880 --> 00:22:05.200 value is continually adjusted for inflation, 00:22:05.480 --> 00:22:08.119 which removes the guesswork. But that's not common 00:22:08.119 --> 00:22:11.079 for most loans. No. So most other lenders must 00:22:11.079 --> 00:22:13.660 either estimate the expected inflation rate, 00:22:13.779 --> 00:22:16.940 which is inherently risky, or they use variable 00:22:16.940 --> 00:22:19.380 floating rates that can be reset periodically 00:22:19.380 --> 00:22:22.539 to adapt to changing price levels. And that estimation 00:22:22.539 --> 00:22:25.579 is tough. We've seen periods like during the 00:22:25.579 --> 00:22:28.019 2011 commodity spike or the high inflation in 00:22:28.019 --> 00:22:30.779 the 1970s where the real rate of return on government 00:22:30.779 --> 00:22:33.259 bonds was actually negative. A painful lesson 00:22:33.259 --> 00:22:35.440 that market expectations are not guarantees. 00:22:35.720 --> 00:22:39.019 The third crucial factor is default risk. or 00:22:39.019 --> 00:22:41.480 creditworthiness. This is the risk that the specific 00:22:41.480 --> 00:22:44.099 borrower will fail to repay the principal and 00:22:44.099 --> 00:22:46.779 interest. This risk demands a risk premium, a 00:22:46.779 --> 00:22:48.740 higher rate to compensate the lender for the 00:22:48.740 --> 00:22:51.319 chance of total loss. This premium is heavily 00:22:51.319 --> 00:22:53.279 dependent on the integrity of the borrower and 00:22:53.279 --> 00:22:55.400 the collateral they offer. Which explains why 00:22:55.400 --> 00:22:58.640 a consumer with a low credit score pays a much 00:22:58.640 --> 00:23:01.000 higher rate than a large corporation. And why 00:23:01.000 --> 00:23:03.240 loans to developing nations carry significantly 00:23:03.240 --> 00:23:05.779 higher risk premiums than loans to established, 00:23:06.019 --> 00:23:08.039 stable governments like the U .S. or Germany. 00:23:08.170 --> 00:23:11.150 And collateral, as you mentioned, matters immensely. 00:23:11.269 --> 00:23:13.809 A secured loan, like a mortgage where the house 00:23:13.809 --> 00:23:16.950 is collateral, will always carry a lower rate 00:23:16.950 --> 00:23:19.670 than an unsecured line of credit. Okay. And finally, 00:23:19.769 --> 00:23:22.230 the fourth factor is the term and liquidity of 00:23:22.230 --> 00:23:25.480 the loan. Term refers to duration. Generally, 00:23:25.539 --> 00:23:27.940 shorter terms have lower default risk because 00:23:27.940 --> 00:23:31.059 the near future is easier to predict. This typically 00:23:31.059 --> 00:23:33.740 results in an upward sloping yield curve. You 00:23:33.740 --> 00:23:36.039 get paid less to lend money for three months 00:23:36.039 --> 00:23:40.220 than for 30 years. Liquidity refers to how quickly 00:23:40.220 --> 00:23:42.819 the lender can resell or liquidate the asset. 00:23:43.180 --> 00:23:45.380 A U .S. Treasury bond is highly liquid and can 00:23:45.380 --> 00:23:47.859 be sold instantly, so it offers a lower return. 00:23:48.279 --> 00:23:51.140 A highly illiquid loan, like seller -financed 00:23:51.140 --> 00:23:53.819 debt on a specialized piece of equipment, demands 00:23:53.819 --> 00:23:56.000 a significant liquidity premium to compensate 00:23:56.000 --> 00:23:58.519 for being locked into that agreement. So if we 00:23:58.519 --> 00:24:01.019 synthesize these four components, we arrive at 00:24:01.019 --> 00:24:03.420 the nominal rate, I, that the consumer sees. 00:24:03.579 --> 00:24:05.440 And there's a formula for this. There is. You 00:24:05.440 --> 00:24:08.900 can express it as... I equals R plus pi plus 00:24:08.900 --> 00:24:11.559 C. So the nominal rate equals the real rate R 00:24:11.559 --> 00:24:14.599 plus expected inflation pi plus the credit risk 00:24:14.599 --> 00:24:16.640 yield spread. Walk me through a real example, 00:24:16.799 --> 00:24:20.259 a 30 -year mortgage. Okay. A bank assesses the 00:24:20.259 --> 00:24:22.619 underlying real rate required by investors, say 00:24:22.619 --> 00:24:26.039 1 .5%. They estimate the average annual inflation 00:24:26.039 --> 00:24:29.759 pie over 30 years, say 3%. And then they add 00:24:29.759 --> 00:24:32.059 a credit risk and liquidity premium C for that 00:24:32.059 --> 00:24:35.279 specific borrower, say 1%. The resulting nominal 00:24:35.279 --> 00:24:39.119 rate I is 1 .5 % plus 3 % plus 1%, which is 5 00:24:39.119 --> 00:24:41.819 .5%. That's the rate you're quoted. That framework 00:24:41.819 --> 00:24:43.599 provides perfect clarity on how the price of 00:24:43.599 --> 00:24:45.740 money is constructed piece by piece. Yeah. Now 00:24:45.740 --> 00:24:48.049 we touched on default risk. But we must clarify 00:24:48.049 --> 00:24:50.369 default interest. Right. Default interest is 00:24:50.369 --> 00:24:52.950 a highly specialized risk premium. It is a much 00:24:52.950 --> 00:24:55.549 higher rate, sometimes dramatically so, that 00:24:55.549 --> 00:24:57.809 is contractually triggered only if the borrower 00:24:57.809 --> 00:24:59.690 commits a material breach of the loan agreement, 00:24:59.849 --> 00:25:01.930 like failing to make a payment. It is essentially 00:25:01.930 --> 00:25:04.190 a penalty rate. It compensates the lender for 00:25:04.190 --> 00:25:06.269 the fact that the borrower has now become high 00:25:06.269 --> 00:25:08.930 risk. The interest rate on the remaining principal 00:25:08.930 --> 00:25:13.190 might jump from 5 % to 15%. However, many jurisdictions 00:25:13.190 --> 00:25:15.710 have complex laws regarding default interest. 00:25:16.029 --> 00:25:19.569 If the rate is deemed excessive, if it penalizes 00:25:19.569 --> 00:25:22.410 the borrower far beyond the actual loss incurred 00:25:22.410 --> 00:25:25.589 by the lender courts can deem the clause unenforceable. 00:25:25.710 --> 00:25:28.029 All these market factors determine the rate in 00:25:28.029 --> 00:25:30.619 a theoretical free market. But the biggest influence 00:25:30.619 --> 00:25:33.500 on rates worldwide is not demand for mortgages, 00:25:33.519 --> 00:25:36.019 but government intervention via the central bank. 00:25:36.200 --> 00:25:38.279 Absolutely. Central banks, like the Federal Reserve 00:25:38.279 --> 00:25:40.319 in the U .S. or the European Central Bank, hold 00:25:40.319 --> 00:25:42.740 immense power over short term rates. It's their 00:25:42.740 --> 00:25:45.599 primary lever of monetary policy. They do this 00:25:45.599 --> 00:25:47.519 by targeting what the U .S. calls the federal 00:25:47.519 --> 00:25:49.920 funds rate. The rate banks charge each other 00:25:49.920 --> 00:25:52.180 for overnight loans. And the main tool they use 00:25:52.180 --> 00:25:54.359 to hit that target rate is called open market 00:25:54.359 --> 00:25:56.660 operations. Could you walk us through the actual 00:25:56.660 --> 00:25:59.240 mechanism? I mean, how does the Fed... Buying 00:25:59.240 --> 00:26:01.839 a bond affect my car loan rate six months later. 00:26:01.960 --> 00:26:05.160 It's a chain reaction. When the Fed decides it 00:26:05.160 --> 00:26:07.539 wants to lower rates to stimulate the economy, 00:26:07.819 --> 00:26:11.079 it buys U .S. Treasury securities from the market. 00:26:11.299 --> 00:26:14.779 Wait, so the Fed is buying bonds. Where does 00:26:14.779 --> 00:26:16.680 the money come from? Are they just creating it? 00:26:17.259 --> 00:26:19.880 In essence, yes. They are crediting the accounts 00:26:19.880 --> 00:26:22.559 of the banks they buy the bonds from. When the 00:26:22.559 --> 00:26:25.500 Fed buys a billion dollars in treasuries, it 00:26:25.500 --> 00:26:28.200 injects a billion dollars of new money into the 00:26:28.200 --> 00:26:31.240 financial system, specifically into the bank's 00:26:31.240 --> 00:26:34.160 reserve accounts at the Fed. So the banks suddenly 00:26:34.160 --> 00:26:37.400 have excess cash lying around in reserves. Precisely. 00:26:37.400 --> 00:26:39.740 They are now sitting on excess reserves, money 00:26:39.740 --> 00:26:42.259 they must use or lend to maximize their return. 00:26:42.480 --> 00:26:45.019 To get rid of this excess liquidity, they lend 00:26:45.019 --> 00:26:47.019 it aggressively to other banks in the overnight 00:26:47.019 --> 00:26:49.160 federal funds market. And more supply means a 00:26:49.160 --> 00:26:52.009 lower price. Exactly. An increased supply of 00:26:52.009 --> 00:26:54.769 funds in that market causes the price, the federal 00:26:54.769 --> 00:26:57.369 funds rate to drop. And since that rate is the 00:26:57.369 --> 00:26:59.390 base cost of borrowing for the entire banking 00:26:59.390 --> 00:27:02.190 system, the lower rate then ripples out, making 00:27:02.190 --> 00:27:04.170 everything from mortgages to corporate bonds 00:27:04.170 --> 00:27:06.690 cheaper. And conversely, if they want to raise 00:27:06.690 --> 00:27:08.730 rates, they sell treasuries, which pulls cash 00:27:08.730 --> 00:27:11.730 out of the system. It pulls cash out, tightens 00:27:11.730 --> 00:27:13.890 reserves, increases the demand for overnight 00:27:13.890 --> 00:27:16.430 lending and forces the federal funds rate higher. 00:27:16.799 --> 00:27:18.960 It proves that while rates are determined by 00:27:18.960 --> 00:27:21.599 real factors, they are heavily managed by monetary 00:27:21.599 --> 00:27:24.559 policy targeting liquidity. That brings us perfectly 00:27:24.559 --> 00:27:27.579 to the final, deepest section of our dive, the 00:27:27.579 --> 00:27:30.359 great debates. We have now defined interest, 00:27:30.599 --> 00:27:33.079 calculated it, and seen how the market prices 00:27:33.079 --> 00:27:35.539 it. But we still haven't fully explained why 00:27:35.539 --> 00:27:38.259 interest must exist. This is where economists 00:27:38.259 --> 00:27:40.759 have fought for centuries. This is where the 00:27:40.759 --> 00:27:44.259 core ideological conflicts lie. If you ask Turgot, 00:27:44.500 --> 00:27:47.839 Keynes or Rothbard why interest exists, you get 00:27:47.839 --> 00:27:50.940 three completely different yet compelling answers. 00:27:51.259 --> 00:27:53.640 Let's start with the earliest scientific explanation 00:27:53.640 --> 00:27:55.900 from the Enlightenment, the French economist 00:27:55.900 --> 00:27:59.480 and Robert Jacques Turgot in 1770 and his fructification 00:27:59.480 --> 00:28:02.180 theory. Turgot, moving away from moral arguments, 00:28:02.380 --> 00:28:04.940 saw a scientific rationale for rates being greater 00:28:04.940 --> 00:28:08.400 than zero based on opportunity cost. A key concept 00:28:08.400 --> 00:28:11.039 we discussed earlier. He compared the loan rate 00:28:11.039 --> 00:28:13.380 to the inherent reproducible return on agricultural 00:28:13.380 --> 00:28:16.500 land or capital. He argued that if money wasn't 00:28:16.500 --> 00:28:18.759 invested in a loan, it could be invested in productive 00:28:18.759 --> 00:28:22.299 land. Yes. And his genius was providing a mathematical 00:28:22.299 --> 00:28:24.680 proof for the necessity of a positive interest 00:28:24.680 --> 00:28:27.660 rate. He focused on the concept of land value 00:28:27.660 --> 00:28:30.859 as a perpetuity, a piece of capital that yields 00:28:30.859 --> 00:28:33.200 revenue indefinitely. How does that math work? 00:28:33.420 --> 00:28:37.059 The value of any perpetual income stream is calculated 00:28:37.059 --> 00:28:39.880 by taking the annual yield and dividing it by 00:28:39.880 --> 00:28:42.539 the prevailing interest rate. If your land yields 00:28:42.539 --> 00:28:46.220 $100 per year and the interest rate is 10%, that 00:28:46.220 --> 00:28:49.799 land is worth $1 ,000. Okay. Turgot argued that 00:28:49.799 --> 00:28:51.640 if the interest rate mathematically approached 00:28:51.640 --> 00:28:54.440 zero, the denominator in that equation would 00:28:54.440 --> 00:28:56.700 approach zero and thus the value of the land 00:28:56.700 --> 00:28:59.200 would approach infinity. A piece of land that 00:28:59.200 --> 00:29:01.960 yields $100 a year would be worth an infinite 00:29:01.960 --> 00:29:04.039 amount of money if the interest rate were zero. 00:29:04.460 --> 00:29:06.980 Turgo argued this was economically and mathematically 00:29:06.980 --> 00:29:10.220 absurd. Therefore, for the entire economic system 00:29:10.220 --> 00:29:13.099 to make sense and for capital assets like land 00:29:13.099 --> 00:29:16.000 to have a positive and finite price, the interest 00:29:16.000 --> 00:29:18.720 rate must remain above zero. Moving forward a 00:29:18.720 --> 00:29:21.279 century, we have a classical theory championed 00:29:21.279 --> 00:29:23.960 by economists like John Stuart Mill, David Ricardo 00:29:23.960 --> 00:29:26.839 and Irving Fisher. They saw the interest rate 00:29:26.839 --> 00:29:29.509 as a market clearing mechanism. The classical 00:29:29.509 --> 00:29:31.990 school argued that the interest rate adjusts 00:29:31.990 --> 00:29:34.430 to maintain equilibrium between the supply of 00:29:34.430 --> 00:29:37.789 loanable funds driven by people saving and the 00:29:37.789 --> 00:29:40.309 demand for loanable funds, which is driven by 00:29:40.309 --> 00:29:42.740 businesses investing. So the interest rate is 00:29:42.740 --> 00:29:44.880 merely the price that balances the desire to 00:29:44.880 --> 00:29:47.660 save with the desire to invest. Correct. And 00:29:47.660 --> 00:29:49.940 the primary regulator of this rate, they argued, 00:29:50.099 --> 00:29:52.980 was the marginal efficiency of capital, or MEC. 00:29:53.559 --> 00:29:56.740 The MEC is the annual revenue yielded by the 00:29:56.740 --> 00:29:59.220 next or extra increment of capital investment 00:29:59.220 --> 00:30:02.140 expressed as a proportion of its cost. So if 00:30:02.140 --> 00:30:04.180 a business expects a new project to yield a 10 00:30:04.180 --> 00:30:07.319 % return, the MEC... They will only borrow money 00:30:07.319 --> 00:30:10.500 as long as the interest rate is below 10%. Precisely. 00:30:10.500 --> 00:30:12.839 They'll keep investing until the borrowing rate 00:30:12.839 --> 00:30:15.799 equals that marginal expected return. The equilibrium 00:30:15.799 --> 00:30:18.059 is achieved when the desired saving function 00:30:18.059 --> 00:30:20.420 intersects the investment schedule. But John 00:30:20.420 --> 00:30:22.160 Maynard Keynes, during the Great Depression, 00:30:22.380 --> 00:30:25.299 famously leveled two major critiques against 00:30:25.299 --> 00:30:28.019 this seemingly neat classical picture. Keynes' 00:30:28.119 --> 00:30:30.839 critique was fundamental. First, he noted that 00:30:30.839 --> 00:30:33.200 the classical theory fails to explain a clear 00:30:33.200 --> 00:30:36.480 real -world observation. Why does an increase 00:30:36.480 --> 00:30:38.460 in the money supply tend to reduce the interest 00:30:38.460 --> 00:30:41.160 rate, at least initially? In their framework, 00:30:41.319 --> 00:30:43.839 money supply is separate from real saving and 00:30:43.839 --> 00:30:46.359 investment. He called this a circular argument. 00:30:46.559 --> 00:30:48.759 Yes. And his second critique was structural. 00:30:49.019 --> 00:30:51.440 The classical theory requires you to know the 00:30:51.440 --> 00:30:53.500 interest rate to determine the scale of investment. 00:30:53.740 --> 00:30:55.880 But the scale of investment is needed to calculate 00:30:55.880 --> 00:30:58.859 the marginal efficiency of capital. He found 00:30:58.859 --> 00:31:01.359 it was a circular dependency that was unsatisfactory 00:31:01.359 --> 00:31:04.519 for explaining real economic cycles. So Keynes 00:31:04.519 --> 00:31:06.900 shifted the focus entirely away from productivity 00:31:06.900 --> 00:31:09.420 and saving towards something purely monetary, 00:31:09.680 --> 00:31:12.640 liquidity preference. Keynes argued that interest 00:31:12.640 --> 00:31:14.680 is determined not by the supply and demand for 00:31:14.680 --> 00:31:17.400 capital, but by the demand for money for liquidity 00:31:17.400 --> 00:31:20.079 and the supply of money created by the central 00:31:20.079 --> 00:31:23.599 bank. Money, unlike a bond, provides immediate 00:31:23.599 --> 00:31:26.420 flexibility and safety. It holds a liquidity 00:31:26.420 --> 00:31:29.829 advantage. And interest, therefore, becomes the 00:31:29.829 --> 00:31:32.210 reward you have to receive for parting with that 00:31:32.210 --> 00:31:34.930 advantage. That's the essence. People demand 00:31:34.930 --> 00:31:38.309 money for three primary motives. The transactionary 00:31:38.309 --> 00:31:41.750 motive, money for day -to -day purchases, the 00:31:41.750 --> 00:31:44.289 precautionary motive, holding cash for emergencies, 00:31:44.710 --> 00:31:48.710 and the speculative motive. holding cash to take 00:31:48.710 --> 00:31:50.509 advantage of future investment opportunities. 00:31:50.910 --> 00:31:53.430 The higher the rate of interest offered, the 00:31:53.430 --> 00:31:55.430 more willing people are to give up their liquidity 00:31:55.430 --> 00:31:58.829 and buy a less liquid asset, like a bond. And 00:31:58.829 --> 00:32:01.069 you mentioned he built on the work of Silvio 00:32:01.069 --> 00:32:03.130 Gassel. We have to acknowledge Gassel. He was 00:32:03.130 --> 00:32:05.750 a 19th century economist who theorized that interest 00:32:05.750 --> 00:32:08.650 is a purely monetary phenomenon. He observed 00:32:08.650 --> 00:32:10.970 that interest existed in monetary economies, 00:32:11.109 --> 00:32:13.930 but seemed absent in pure barter economies. And 00:32:13.930 --> 00:32:16.109 his theory was that money doesn't spoil. Right. 00:32:16.460 --> 00:32:19.119 Unlike grain or milk, money doesn't incur storage 00:32:19.119 --> 00:32:21.140 costs, which gives it a significant advantage. 00:32:21.720 --> 00:32:24.140 Keynes recognized this insight, but clarified 00:32:24.140 --> 00:32:26.359 the specific advantage of money as liquidity, 00:32:26.619 --> 00:32:29.740 the ease of exchange and reduced risk, which 00:32:29.740 --> 00:32:31.619 is why people are willing to pay a premium or 00:32:31.619 --> 00:32:34.059 interest to borrow it. Moving on, we have the 00:32:34.059 --> 00:32:36.680 Austrian School of Economics, represented by 00:32:36.680 --> 00:32:39.279 Murray Rothbard, who rejected the entire focus 00:32:39.279 --> 00:32:41.839 on the loan market as being, well, secondary. 00:32:42.349 --> 00:32:44.450 The Austrian theory argues that the loan market 00:32:44.450 --> 00:32:47.410 rate is merely a symptom, a manifestation of 00:32:47.410 --> 00:32:50.109 a far deeper pre -existing economic reality, 00:32:50.369 --> 00:32:54.269 the natural phenomenon of time preference. Time 00:32:54.269 --> 00:32:56.950 preference being the psychological reality that 00:32:56.950 --> 00:32:59.569 humans prefer goods in the present over the exact 00:32:59.569 --> 00:33:02.230 same goods in the future. Absolutely. If I offer 00:33:02.230 --> 00:33:04.750 you a glass of water now or two glasses of water 00:33:04.750 --> 00:33:07.170 next week, most people will take the single glass 00:33:07.170 --> 00:33:10.640 now. That inherent preference for present satisfaction 00:33:10.640 --> 00:33:13.759 is reflected in all economic decisions. Rothbard 00:33:13.759 --> 00:33:16.160 argued that focusing solely on bank loans misses 00:33:16.160 --> 00:33:18.799 the fundamental point. So where do they see the 00:33:18.799 --> 00:33:21.140 real rate of interest reflected, if not in a 00:33:21.140 --> 00:33:23.200 bank contract? They see it in the price spreads 00:33:23.200 --> 00:33:25.880 between the various stages of production. Think 00:33:25.880 --> 00:33:28.259 of it this way. Consumers goods, like a finished 00:33:28.259 --> 00:33:31.619 cake, are present goods. Producers goods, like 00:33:31.619 --> 00:33:33.980 the oven and the flour, are future goods used 00:33:33.980 --> 00:33:36.720 to create the present good later. The cost difference 00:33:36.720 --> 00:33:39.579 between buying the finished product today versus 00:33:39.579 --> 00:33:42.539 buying the means to produce it reveals the time 00:33:42.539 --> 00:33:44.920 preference of society. That's the Austrian insight. 00:33:45.079 --> 00:33:47.380 The price spread between the raw material stage 00:33:47.380 --> 00:33:49.920 and the finished product stage is the true natural 00:33:49.920 --> 00:33:53.400 rate of interest. This rate, driven by human 00:33:53.400 --> 00:33:56.140 psychology, then trickles down and determines 00:33:56.140 --> 00:33:59.200 the rate banks must charge. They criticized Keynes 00:33:59.200 --> 00:34:01.740 for ignoring this fundamental psychological reality. 00:34:02.220 --> 00:34:04.990 Finally, let's bring in Nutwicksell. whose work 00:34:04.990 --> 00:34:07.589 provided a comprehensive theory linking the real 00:34:07.589 --> 00:34:10.269 economy to the monetary one, distinguishing between 00:34:10.269 --> 00:34:13.210 the natural rate and the nominal rate. Wicksell, 00:34:13.429 --> 00:34:16.929 writing around 1898, introduced a crucial distinction. 00:34:17.530 --> 00:34:20.090 The natural rate is the hypothetical equilibrium 00:34:20.090 --> 00:34:22.309 rate of interest that would exist in a purely 00:34:22.309 --> 00:34:25.130 barter economy. The rate determined purely by 00:34:25.130 --> 00:34:27.449 real factors like productivity and time preference. 00:34:27.710 --> 00:34:29.710 It's what the rate should be. And the monetary 00:34:29.710 --> 00:34:31.829 rate is what banks actually charge in a cash 00:34:31.829 --> 00:34:35.159 economy. Yes. And Wicksell's major insight was 00:34:35.159 --> 00:34:36.880 that when the monetary rate diverges from the 00:34:36.880 --> 00:34:40.239 natural rate, economic instability results. If 00:34:40.239 --> 00:34:42.300 the central bank pushes the monetary rate below 00:34:42.300 --> 00:34:44.619 the natural rate, making borrowing too cheap, 00:34:44.659 --> 00:34:47.280 it encourages excessive investment and credit 00:34:47.280 --> 00:34:50.860 expansion, causing inflation to rise. And conversely, 00:34:50.860 --> 00:34:53.099 if the central bank holds the monetary rate above 00:34:53.099 --> 00:34:55.920 the natural rate, it stifles investment and saving, 00:34:56.119 --> 00:34:58.539 leading to economic contraction and deflation. 00:34:59.079 --> 00:35:02.030 Wicksell's work was hugely influential. It provided 00:35:02.030 --> 00:35:04.469 the conceptual framework for later theories and 00:35:04.469 --> 00:35:06.710 demonstrated how the actions of a central bank 00:35:06.710 --> 00:35:09.210 can either stabilize the economy by aligning 00:35:09.210 --> 00:35:11.789 the monetary natural rates or destabilize it 00:35:11.789 --> 00:35:14.489 by creating divergence. It is truly fascinating 00:35:14.489 --> 00:35:17.550 that the same phenomenon interest can be attributed 00:35:17.550 --> 00:35:20.909 simultaneously to Turgot's mathematical requirement, 00:35:21.170 --> 00:35:24.909 to King's concern about liquidity, or to Rothbard's 00:35:24.909 --> 00:35:26.969 deep psychological theory of time preference. 00:35:27.250 --> 00:35:29.869 It underscores the complexity. Interest isn't 00:35:29.869 --> 00:35:32.019 just one price. It's a reflection of productivity, 00:35:32.320 --> 00:35:35.300 risk, expectation, and human psychology all rolled 00:35:35.300 --> 00:35:38.260 into one. That brings us to our conclusion. We've 00:35:38.260 --> 00:35:40.159 navigated a journey from a simple definition, 00:35:40.380 --> 00:35:43.519 tracing its moral struggle back to Sumerian grain 00:35:43.519 --> 00:35:46.019 loans, through the precise mathematics that led 00:35:46.019 --> 00:35:48.539 to the discovery of the constant E, detailing 00:35:48.539 --> 00:35:50.599 how market risk and central bank intervention 00:35:50.599 --> 00:35:54.099 construct the final price, and finally, examining 00:35:54.099 --> 00:35:56.460 the deep, conflicting economic theories that 00:35:56.460 --> 00:35:59.159 still drive global policy decisions today. And 00:35:59.159 --> 00:36:01.219 before we wrap, let's just revisit the idea of 00:36:01.219 --> 00:36:03.340 an interest -free economy like modern Islamic 00:36:03.340 --> 00:36:06.400 finance. While they successfully remove ruba, 00:36:06.440 --> 00:36:08.599 the pure predetermined component of interest, 00:36:08.880 --> 00:36:11.159 it is important to remember that financial institutions 00:36:11.159 --> 00:36:14.659 still incur costs and risks. Right. We established 00:36:14.659 --> 00:36:16.780 earlier that the total interest rate is actually 00:36:16.780 --> 00:36:19.639 composed of four parts. Pure interest, a risk 00:36:19.639 --> 00:36:22.199 premium, inflation expectations, and administrative 00:36:22.199 --> 00:36:25.420 costs. In a Sharia compliance system, the pure 00:36:25.420 --> 00:36:28.179 risk -free interest component vanishes by definition. 00:36:28.519 --> 00:36:31.019 But the financial institution still needs to 00:36:31.019 --> 00:36:33.800 cover its administrative costs and still deserves 00:36:33.800 --> 00:36:36.179 compensation for sharing in the risk, which is 00:36:36.179 --> 00:36:39.000 the risk premium. This compensation is simply 00:36:39.000 --> 00:36:41.320 structured as a profit share or a lease payment 00:36:41.320 --> 00:36:44.380 rather than a fixed interest rate. So financial 00:36:44.380 --> 00:36:47.420 activity continues just under a different shared 00:36:47.420 --> 00:36:50.849 risk. which brings us back full circle to the 00:36:50.849 --> 00:36:53.030 philosophical and psychological root of all these 00:36:53.030 --> 00:36:56.639 debates. the value of time. The theories we explored, 00:36:56.739 --> 00:36:59.199 from the need to compensate a lender for deferred 00:36:59.199 --> 00:37:01.420 consumption to the innate desire for immediate 00:37:01.420 --> 00:37:04.400 satisfaction, they all boil down to pricing time 00:37:04.400 --> 00:37:06.920 itself. Indeed. It's not just about money. It's 00:37:06.920 --> 00:37:09.360 about human nature. Every economic decision you 00:37:09.360 --> 00:37:11.619 make, whether to take a lump sum now or wait 00:37:11.619 --> 00:37:13.760 for a larger annuity later, whether to pay off 00:37:13.760 --> 00:37:15.900 debt early or stretch out the payments, is an 00:37:15.900 --> 00:37:17.860 expression of your personal time preference. 00:37:18.199 --> 00:37:20.579 So we leave you, the listener, with this final 00:37:20.579 --> 00:37:23.139 provocative thought. Given that interest is rooted 00:37:23.139 --> 00:37:25.780 in the intrinsic human desire for instant gratification, 00:37:26.099 --> 00:37:29.079 preferring a good now rather than later, every 00:37:29.079 --> 00:37:31.420 time you accept or charge an interest rate, you 00:37:31.420 --> 00:37:34.119 are putting a tangible dollar value on your willingness 00:37:34.119 --> 00:37:36.900 to pay or be paid to wait. What does your own 00:37:36.900 --> 00:37:39.219 personal preference for time reveal about your 00:37:39.219 --> 00:37:41.500 economic philosophy? And how will that dictate 00:37:41.500 --> 00:37:43.539 your financial choices moving forward? Thank 00:37:43.539 --> 00:37:44.800 you for joining us for this deep dive.