Welcome back to the Deep Dive. Today we are really
getting into the foundations of modern personal
finance. We're tackling a concept that on the
surface seems so straightforward. Deceptively
so. Right. The fixed rate mortgage. But what
we found is that it contains this surprising
amount of financial mathematics, some really
compelling history and wild global variations.
It really is that three letter acronym, FRM,
that millions of homes are built on. And yet,
as we synthesize the material, we just kept coming
back to the fact that the very definition of
fixed is, well, it's not universal at all. Not
even close. So if you're tuning in thinking this
is just a quick chat about a static interest
rate, you are in for a serious look at how time,
inflation, and just plain geography can completely
transform this one product. So our mission today
is to provide you, the listener, with a kind
of comprehensive shortcut. We want to move way
beyond the basic dictionary definition. Absolutely.
We want to get into the origin story. I mean,
why was this loan even invented in the first
place? And then the precise mechanics of the
calculation. The math. The inherent risks that
come with, you know, 15 or 30 years of supposed
stability and how the entire concept just shifts
the moment you cross a national border. So let's
start at the absolute core because that definition,
even the simple one, is crucial. A fixed rate
mortgage is a mortgage loan where the interest
rate stipulated on the note remains constant.
It's fixed. Fixed for the whole time. For the
entire agreed upon term of the loan, no changes.
And that right there is the immediate benefit.
It's the fundamental reason this product exists
and why it dominates markets like the U .S. and,
as we found out, Denmark of all places. It's
all about budgetary predictability. Exactly.
Because that interest rate is fixed, your monthly
payment is fixed, and the loan duration is fixed.
It's a trifecta of certainty. And that level
of certainty allows for long -term financial
planning, that is. Right. Well. It's just impossible
with most other loan products out there. That
certainty really is the benchmark, isn't it?
When you look at the whole landscape of borrowing,
the sheer variety is staggering. The FRM just
stands out for that complete fixation. It provides
a kind of bedrock of security. especially in
a housing market that can be incredibly volatile.
And I think it's important to frame the FRM by
looking at its competition, both now and historically.
We're not just talking about the modern adjustable
rate mortgage, the ARM, where the rate floats
or tracks an index. No, the history is key. The
FRM was a truly revolutionary answer to the,
frankly, dangerous instability of the balloon
payment mortgage. I've heard of these, but they
sound terrifying. They were. It was a structure
that forced borrowers to face this massive lump
sum payment at the end of the term. You'd pay
interest for a few years and then, boom, the
whole principle was due. And if you couldn't
pay it? It often led to widespread financial
collapse, foreclosures everywhere. And even today,
the FRM offers security against much riskier
products that, believe it or not, still exist,
like the negative amortization mortgage. Oh,
that's literally the opposite of the FRM's safety.
it's a scary concept it is in a negative amortization
loan your required monthly payment doesn't even
cover the full interest that's due for the month
So your loan balance actually goes up over time,
even while you're making payments. Exactly. You're
digging yourself deeper into debt every single
month. The FRM, by contrast, is engineered from
the ground up for disciplined, complete debt
retirement. Indeed. We are really unpacking a
product that was built for stability and for
long -term planning. And every single feature
of it, from its mathematics to its standardization,
it all reinforces that one central goal. OK,
so to really understand a fixed rate mortgage,
we have to look under the hood. There are these
four constant variables that lock the loan in
place and allow for that calculation of the fixed
monthly payment. What are those four pillars?
Right. These are the constants that the lender
uses to define your entire amortization schedule.
So first, you have the amount of the loan. That's
the principle, what we call PLRs1, the initial
capital you borrowed. Simple enough. Second,
the interest rate. or Tweedles. That's the percentage
of being charged. Third, and this one is sneakily
important, is the compounding frequency. What
do you mean by that? It just defines how often
the interest is calculated and then add it back
to the principal. And fourth, of course, is the
duration of the loan or no dollar, the overall
term, usually in months or years. That third
point, the compounding frequency, is so critical
because it immediately shows how the rules can
change globally, even for the exact same concept.
In the U .S., we just assume monthly compounding.
It's the standard for all the examples you see.
But the research highlights that in a market
like Canada, for instance, interest is typically
compounded semi -annually, so every six months.
So what does that actually mean for the borrower?
It's a subtle change. But it means that even
if a U .S. borrower and a Canadian borrower got
the exact same nominal interest rate, say 5%,
the internal math of their loans, and therefore
the actual amount of interest they pay, will
be different. Because the frequency of that compounding
fundamentally alters the path of the debt. It's
one of those details that has a huge impact over
25 or 30 years. Okay, so now that we have the
constants, let's talk about the giant vulnerability.
The thing that's created precisely because the
loan is fixed for, say, 30 years. Inflation risk.
Inflation risk. This is where that simple idea
of stability gets really complicated really fast.
It really does. It creates the core paradox of
the FRM. When a borrower commits to a fixed dollar
payment for up to three decades, they are introducing
this massive variable into the equation. Which
is the future real value of that dollar. Precisely.
The lender is vulnerable if the dollar loses
value, and the borrower is vulnerable if the
dollar unexpectedly gains value. Let's break
down the two main scenarios that really show
this inflation paradox. First, the high inflation
scenario. This is the borrower's dream scenario,
really. If inflation rises unexpectedly and sharply,
let's say it jumps from 2 % to 8%, the person
with the fixed rate mortgage benefits tremendously.
Why is that? Because inflation erodes the real
present value of those fixed loan repayments.
You're paying back the debt with dollars that
have way less purchasing power than the dollars
you borrowed years earlier. So your debt is shrinking
in real terms. Exactly. The real debt burden,
especially measured against your income, which
is hopefully rising with inflation, shrinks dramatically.
It's a mechanism that effectively transfers wealth
from the lender to the borrower during periods
of high, unexpected inflation. That is just a
stunning realization for a lot of people. The
stability you bought is actually a massive hedge
against a rising cost of living. It absolutely
is. But the tradeoff, the flip side of that coin,
is the second scenario, the low interest rate
scenario. And this is where the borrower can
get hurt. If economic conditions improve or if
inflation suddenly drops, and that leads to significantly
lower interest rates across the whole financial
market. So let's say new mortgages are being
issued at 3%, but you're locked in at 6%. You're
worse off, much worse off. You're locked into
an uncompetitive higher rate. and potentially
for decades. You bought that certainty. But in
this scenario, certainty means you're missing
out on all this cheaper capital. You'd have to
pay a massive refinancing cost to access that
lower rate, which could wipe out a lot of the
potential savings. And this brings us right to
the general market principle about the cost tradeoff.
Lenders, they're not dumb. They understand they're
absorbing 30 years of inflation risk when they
issue an FRM. So they price that risk in from
the start. Of course. And that's why FRMs almost
universally charge a higher starting interest
rate compared to comparable adjustable rate products
or ARMs. So the premium you pay on day one, that
slightly higher rate, it's literally an insurance
premium. That's the perfect way to describe it.
You are paying the lender for the peace of mind
that they, not you, will bear. the financial
pain if rates jump dramatically over the next
few decades. And this inherent trade off, it
informs a really critical piece of scholarly
advice that came up in the sources. Yeah, this
was fascinating. The data suggests that as a
general rule, borrowers should generally prefer
adjustable rate over fixed rate mortgages unless
interest rates are low. OK, that's a powerful
insight. Let's unpack that. Well, if current
rates are historically high, the potential for
them to fall is much greater than the potential
for them to keep climbing indefinitely. Right.
What goes up must come down eventually. In that
scenario, flexibility, the ARM, offers the greatest
potential reward. But if rates are already near
historic lows, the risk of them increasing dramatically
is much higher than the risk of them falling
further. So that's when you buy the insurance.
That's when the FRM, the expensive insurance,
becomes a really smart, necessary hedge. Okay.
So when a borrower is thinking about the true
cost of their mortgage, they have to look at
three long -term components. First is the original
loan principle, the P dollar. And you've got
all the expenses, taxes, insurance, closing fees,
all of that. And the third, and this is where
the real leverage is, is the total interest that
you'll pay over the life of the loan. That's
the number that can be... Truly staggering. And
that leads us to a fascinating piece of analysis
from the source material, what we're calling
the rate term puzzle. We all tend to obsess over
the interest rate, right? Completely. It's the
headline number. But the sources present these
compelling examples showing that the duration
of the loan, that no dollar variable, can be
exponentially more important than the rate, $3.
Absolutely. The research offers a shocking...
completely counterintuitive revelation about
the total final dollar cost of the loan. Okay,
so listen to this because this one really made
me stop and think. A loan structured at 2 .5
% interest for 30 years results in the exact
same final total dollar cost as a loan at 5 %
interest for 15 years. It's wild, isn't it? It's
insane. And to show this isn't just a weird anomaly,
they give another example. A loan at 5 % interest
for 30 years has the exact same total cost as
a loan at 10 % for 15 years. Let that sink in.
Double the interest rate. But because you cut
the term in half, you pay the exact same amount
of money in the end. I have to pause there. I
mean, I spend so much time focusing on trying
to shave half a percentage point off the rate.
But you're telling me that doubling the interest
rate from 5 % to 10 % doesn't increase my total
debt burden as long as I cut the term in half?
That is precisely what the financial mathematics
show. It means long -term expense is disproportionately
weighted toward the term length, the dollar.
So the time is more important than the rate?
Much more important. If you can significantly
reduce the duration of time that the principle
is outstanding, you completely neutralize what
appears to be a massive percentage rate hike.
But why? What is it about that time factor that
gives it such overwhelming weight? It's the raw
power of compound interest applied over decades.
In that 30 -year scenario, the interest is compounding
on the outstanding principal balance 360 times.
By cutting the term to 15 years, you are slashing
the number of compounding periods in half down
to just 180. Even if the interest rate you're
paying each period is much higher, the simple
fact that you stopped that compounding clock
so much earlier saves you an astronomical amount
of money. So when a new borrower is sitting down,
they should be prioritizing finding the shortest
possible term they can actually afford, even
if it means accepting a slightly higher headline
interest rate. The math says yes, because the
time savings will dramatically outweigh the rate
difference over the life of the loan. It just
reveals this profound financial truth, doesn't
it? The monthly payment is all about affordability
today, but the total cost of the debt is overwhelmingly
driven by the term length. Which means the 30
-year mortgage, while it offers the lowest monthly
burden and is the most popular for that reason,
is often the most expensive path to homeownership
in the long run. By a lot. Okay, so now that
we understand the math and the risk baked into
the FRM structure, let's look at its revolutionary
history. This product, as we know it, was essentially
invented in the United States. That's right.
And it was invented as a solution to a massive
economic problem. So we need to go back in time
a bit. We need to go back to the 1920s and early
1930s. The prevailing form of mortgage back then
was the balloon payment mortgage we mentioned
earlier. The one where you pay the whole principal
at the end. Exactly. It was a non -amortizing
loan. You only pay the interest every month.
And the entire principal was due as a lump sum
after, say, five to ten years. That sounds inherently
risky, especially during an economic downturn.
It was devastating. Just imagine the Great Depression
hitting. Your five -year term expires in 1932.
You're required to pay the entire principal back,
but you have no equity built up. And the entire
banking system is collapsing. So there's no way
to get a new loan. Banks. weren't lending, you
couldn't refinance. This refinancing risk caused
widespread foreclosures, not because people couldn't
make their monthly interest payments, but because
they couldn't possibly meet that one final balloon
payment. Wow. So the instability of the housing
market in the 1930s, where entire neighborhoods
could be wiped out by a single balloon payment
default, that created the urgent need for a better
product. And that's where the Federal Housing
Administration, the FHA, became instrumental.
They helped develop, and this is the crucial
part, standardize the FRM by insuring these new
fully amortized loans. So the FHA insurance gave
lenders confidence. Total confidence. They knew
they wouldn't lose everything if the borrower
defaulted, which finally allowed them to offer
these lower -risk, long -term, fixed products
to the public. And this was really the birth
of the fully amortized loan structure as we know
it. It was. The loan was engineered from the
start to be completely paid off. principal and
interest by the end of the term. This broke that
terrible cycle of successive loans and constant
high stakes refinancing that had defined the
previous generation of homeownership. It was
a massive societal shift towards financial security.
And those classic U .S. terms, the 15 year and
30 year mortgages, they became the foundational
model for decades. The gold standard, really.
But the U .S. model isn't static. The research
notes that in really high cost housing areas,
you know, especially along the coast. Where a
standard 30 year term still leaves the monthly
payments completely out of reach for average
families. In those areas, we are seeing these
controversial new variations pop up. We're talking
about the emergence of 40 -year and even 50 -year
mortgages. 50 years, that's a lifetime. It's
a painful realization of the affordability crisis.
Lenders are using the only lever they have left,
the dollar variable, the duration, to make the
monthly payment small enough for the borrower
to qualify. But as we just discussed with the
rate term puzzle. While this achieves affordability
today, it dramatically increases the total cost
of interest over the lifespan of the loan. By
hundreds of thousands of dollars, potentially.
It's solving an immediate problem by creating
what is essentially a generational debt burden.
OK, so let's take that benchmark, the 30 -year
fully fixed loan, and travel the world. Because
the moment you step outside of the U .S. and
a few other specific countries, the term fixed
rate mortgage suddenly becomes, well... It really
does. Let's start with our neighbors to the north,
Canada. Their system is fundamentally different.
How so? In Canada, while the mortgage maturity
period is commonly 25 years, the rate itself
is typically only locked for a maximum of 10
years. Often it's only 5. Wait, so what happens
after 10 years? The Canadian homeowner must,
by necessity, renegotiate and refix their rate
two or three times over the life of their mortgage.
That introduces some serious stress. The certainty
of your payment is only guaranteed for the first
few years. Exactly. At the end of that 10 -year
term, they face what is essentially a financial
crossroads. They have to absorb whatever the
prevailing interest rates are at that moment.
They trade long -term security for what is often
a slightly lower rate during that initial fixed
period. Now contrast that instantly with Denmark.
Denmark stands out as one of Europe's true anomalies.
The 30 -year FRM, the American gold standard,
is the... default standard form of home loan
there. Their system is built for that exact same
long -term stability the FHA engineered back
in the 1930s. So it's not just an American thing.
No, it's a Danish thing too. Okay, shifting to
Asia, let's look at Singapore. What does fixed
rate mean there? In Singapore, the interest rate
is fixed only for a very short initial period,
usually just the first three to five years of
the loan. And crucially, after this short fixed
period expires, the loan automatically converts
to a variable floating rate structure. So in
Singapore, the FRM is just an introductory product.
It's used to provide stability during the homeowner's
crucial early years of ownership. And after that,
the borrower takes on all the rate risk themselves.
That's it. And we see a similar, though slightly
different pattern in the United Kingdom. The
UK, right. In the UK, when they use the term
fixed rate mortgage. They are almost always referring
to an adjustable rate mortgage where the rate
is just locked for a short introductory period,
usually between two and five years. Two to five
years. That's barely enough time to settle in.
What happens when that fixed period ends? Because
of that short lock -in period, the UK market
is characterized by incredibly high rates of
refinancing. Borrowers tend to switch products
every few years, jumping from one fixed introductory
product to the next. So they're playing a continuous
game of financial musical chairs. That's a great
way to put it. Hoping they lock in a new rate
before the market spikes. This raises a really
important question. Why? Why does the UK market
favor this short -term fixation over the long
-term certainty we see in the US and Denmark?
The answer is structural, and it's tied to the
history of their primary lenders, the building
societies. Building societies. Like credit unions.
Sort of. Historically, they've been required
to fund at least 50 % of their lending capital
through deposits from their members. This means
they are largely borrowing money short term.
And if they're borrowing money short term, but
they're lending it out long term at a fixed rate,
that creates a huge problem if the central bank
raises rates. Precisely. It creates what's called
an asset liability mismatch. Think of it this
way. They are paying a fluctuating short -term
rate to their depositors. That's their liability.
But they are earning a fixed long -term rate
from their borrowers. That's their asset. And
if the liability cost goes up but the asset income
stays flat, they're in trouble. Big trouble.
If their short -term borrowing costs suddenly
spike, if they have to pay depositors 5 % interest
but their fixed loan is only earning them 4%,
their business model is instantly unprofitable,
maybe even insolvent. Okay, that explains why
lenders in the UK would prefer variable rates.
It transfers that interest rate risk right back
to the borrower, which helps the lender balance
their books against market changes. And that
lender preference, over time, it filters down
to consumer preference. You couple that with
the common desire for the lowest possible initial
monthly payment, and the short -term fixed loan
became the dominant market structure in the UK.
Our final stop on the world tour is Australia,
which offers a fascinating hybrid. Their market
includes what they call honeymoon mortgages.
Right. These are introductory products with really
short periods, sometimes only a year. And what's
unique is that the fixed element might not even
be a fixed rate per se. What is it then? It could
be a fixed reduction in the interest rate for
that period. So you might get a fixed 1 % discount
off the standard variable rate, but only for
the first year. And the Australian product is
often highly flexible, which seems contradictory
to the whole fixed rate concept. It is. The Australian
mortgage model often combines these introductory
rate structures with some powerful, flexible
features. The most common is the ability for
borrowers to overpay their mortgage principal
without any penalty. Which, as we know, saves
a ton on interest. A ton. But here's the kicker.
They are also allowed to... redraw those overpayments
later if they need access to that capital for
an emergency or an investment. So it's like a
line of credit built into your mortgage. In a
way, yes. The Australian system provides this
short -term incentive, but it integrates a flexibility
that lets the borrower manage their own risk
and liquidity against the rigidity of that initial
fixed structure. It just underscores your earlier
point, doesn't it? In global finance, you have
to always ask, how fixed and for how long? Because
the answer changes drastically depending on the
historical context and the prevailing regulatory
pressures of that country's financial system.
All right. Let's pivot back to that central choice
facing any borrower in any market. Fixed versus
adjustable. We've established that the FRM is
usually more expensive than the ARM, at least
initially. Right. But we need a deeper dive into
the why of that cost difference because I think
it helps frame the entire risk transfer mechanism.
The fundamental reason that long -term FRMs are
priced higher than short -term or adjustable
products is all explained by a financial concept
called the yield curve. Okay, let's unpack that.
What does the yield curve tell us about interest
rates? The yield curve is basically just a line
on a graph. It plots the interest rates or yields
of bonds or loans that have the same credit quality
but different maturity dates. And generally,
in a normal... healthy economy, that curve slopes
upward. Meaning? Meaning the longer the term
of the loan, the higher the interest rate offered.
Lenders require more compensation, a premium,
to lock up their capital for 30 years versus
locking it up for, say, one year. Because time
is money. Time is risk, specifically interest
rate risk and inflation risk. Lenders have to
be compensated for that extended uncertainty.
So the higher starting rate on the FRM isn't
arbitrary at all. It's just a reflection of the
standard upward slope of the yield curve. We
should probably quickly mention the rare exception,
though. Of course. That would be the inverted
yield curve, which is when short -term rates
become higher than long -term rates. It sometimes
signals that a recession might be coming. But
the default expectation, the one that justifies
the FRM's higher starting cost, is that time
and duration equal greater expense. So this higher
starting rate on the FRM is therefore the price
you pay for a complete risk transfer. You, the
borrower, are handing all of that interest rate
risk over to the lender. That's it. If rates
rise dramatically, the ARM borrower faces escalating
payments, but the FRM borrower's payment remains
completely constant. The fundamental decision
then becomes... Are you willing to pay a known
premium today for total certainty over three
decades? Or are you willing to accept the risk
of future rate hikes for the potential to save
money if rates fall or stay stable? It's a decision
that's impossible to make perfectly because you'd
have to predict the future. However, financial
economists have studied this decision extensively
over long periods. What does the data tell us
about who wins this gamble most often? The findings
revealed through these really comprehensive studies
are genuinely surprising to a lot of people.
The majority of borrowers who choose adjustable
rate mortgages, the riskier product, end up saving
money in the long term compared to their fixed
rate counterparts. OK, that is a critical finding
for anyone listening who is considering a mortgage.
The data suggests that for the average borrower,
statistically, flexibility pays off. It does,
but... And this is a very important, but we have
to immediately balance that finding. Okay. The
same studies clearly conclude that a significant
subset of ARM borrowers ends up paying significantly
more. sometimes dramatically more than if they
had just chosen the fixed rate product. And when
does that happen? It happens when rates spike
unexpectedly and then stay elevated for longer
than the borrower can withstand. That's what
often leads to default or forced sales. And this
is where we have to bring in the real world context
of risk realization. Yeah. The ARM was the product
that played a central role in the 2008 financial
crisis. A huge role, especially when it was combined
with some very lax underwriting standards. Right.
In the run up to 2008, a lot of people were sold
these teaser rate ARMs. The initial low rate
only lasted two or three years before it reset
or adjusted to a much higher, often crippling
interest rate. They took the risk, but the spike
in rates was combined with falling home values.
A perfect storm. It left them unable to refinance
or sell. The risk that's inherent in an ARM that
a catastrophic payment increases, it was realized
for millions of people. and it led to widespread
financial ruin. That history is why this choice
is so profound. The choice for you, the listener,
it balances the high probability of saving some
money, that's the majority outcome, against the
low probability, but incredibly high impact,
risk of catastrophic financial distress. That's
the minority outcome. So the ultimate conclusion
for the listener facing this fixed versus adjustable
choice is really a psychological and a practical
one. How so? If current rates are historically
low, the FRM is probably worth the higher premium
because the risk of future rates increasing is
quite high. If current rates are historically
high, the ARM offers the best potential for savings.
But only if you have a high tolerance for risk
and a really substantial financial buffer to
absorb a temporary or even a long -term spike
in your payments. It forces you to define your
personal risk appetite. The FRM is the financial
safe harbor. The ARM is the high -risk, high
-reward vessel. So we've talked conceptually
about that fixed monthly payment, $6 ,000 now.
Now we get to move into the engine room, the
actual mathematics that generates that exact
number. This is where the principles of finance
meet calculus, ensuring that after exactly $9
payments, the remaining debt is precisely zero.
The fixed monthly payment is the result of a
very precise formula that calculates the amount
needed to fully amortize the loan. It is the
one constant payment that ensures the principal,
plus all the accrued interest, is paid off exactly
by the final day of the loan's term. Okay, let's
clearly define the three necessary inputs for
the calculation. These are the characteristics
we mentioned earlier. First, we have P dollars
of principal, the amount you borrowed. Then we
have no dollars, the number of monthly payments.
So that's the term of the loan. In months, for
our classic 30 -year FRM example, no dollars
is 30 times 12, so 360 payments. And the most
important variable to get right is $3, the monthly
interest rate. People often confuse this with
the advertised annual percentage rate. Or APR.
And they absolutely should not. That's a huge
mistake. If the yearly nominal interest rate
is, say, 6 .5%, you must first convert that to
a decimal, so .065, and then divide it by 12
to get the monthly interest rate, $3. That's
the actual number used in the compounding math.
If you miss that step. The entire calculation
is off by an order of magnitude. It's completely
wrong. Okay, let's walk through this specific
example from the source material to make this
intimidating math a bit more tangible for everyone
listening. Let's do it. We'll use the numbers
provided. A principal. P dollars of $200 ,000,
a fixed yearly nominal interest rate of 6 .5%,
and a term of 30 years, so $1 to $360 payments.
So if we input $2, which is 0 .65 divided by
12, and no dollars, which is 360, and $200 ,000
into the amortization formula, which is basically
the present value formula for an ordinary annuity,
just rearrange to solve for the constant payment
zero. The calculation spits out a very precise
fixed monthly payment of those dollars of those
$1 ,264 .147. And that single number, $1 ,264
.146, is the foundation of the borrower's entire
30 -year commitment. It's what keeps the whole
structure in equilibrium. Right. And while professionals
will just use the PMT function in a spreadsheet,
understanding the derivation of the formula is
what perfectly illustrates the amortization process
itself. The derivation shows three key components
of how the loan actually works over time. The
first is just the simple dependent structure.
Yes. The formula clearly shows that the LARs
cannot exist without $2 and non -LARs. If the
amount you borrow goes up, your monthly payment
goes up. If the rate goes down, the payment goes
down. If you extend the term, the payment goes
down. But the total cost goes way up. Exactly.
It shows that instantaneous link between those
three inputs and the required payment. The second
and most critical component is how the amount
you owe changes every single month. This is the
heart of amortization. So let's look at the remaining
principle after the very first month, which we'll
call P $. P $ is simply the principle you started
with. P $ plus one month of interest accrued
on that full amount minus your fixed monthly
payment, $2. So every month that fixed payment
tiler arrives and that payment gets split into
two parts. Immediately. The first part of your
tiler payment covers the accrued interest for
that month. You can think of this part as renting
the bank's money for that month. And the second
part, whatever's left over, that goes toward
reducing the actual principal you owe. That's
the buying component. That's the equity you're
building. And because the interest in the early
years is calculated on a very large outstanding
principal, the vast majority of your fixed payment
in the first few years goes toward interest.
And only a tiny sliver goes toward principal
reduction. A tiny sliver. The analogy holds.
In the early years, you were basically just renting
the money. But as the years go by, the outstanding
principal slowly decreases, which means the amount
of interest you owe each month also decreases.
So a steadily larger proportion of that constant
monthly payment sortie shifts over to paying
down the principal. That is the beautiful linear
reduction of debt that characterizes full amortization.
By year 25 of a 30 -year loan, the majority of
your $12 ,264 .44 payment is going toward buying
your equity, and only a small portion is paying
for interest. And the third key component illustrated
by the derivation is the endpoint condition.
The fixed payment is meticulously chosen to guarantee
that the final remaining principal after the
final payment, P .N. DeFi, is exactly zero. This
is the mathematical guarantee that the FRM provides.
It means the amortization formula is the financial
engine that calculates the precise constant required
to ensure total debt retirement at the agreed
upon deadline. It provides that security that
was just missing from the financial landscape
before the FHA standardized this structure. It's
truly the culmination of time, interest, and
principle, all managed by one precise constant
number for... 30 long years. So as we conclude
this deep dive, we've really tracked the fixed
rate mortgage from its origins as this revolutionary
safety product in the 1930s. All the way through
the complexities of its math. To its wildly varied
application across all these different countries.
And that stability of the U .S. and Danish long
term fixed rate is just such a sharp contrast
to the short term refinancing heavy models of
Canada and the U .K. It really is. But in every
single market. The core tradeoff remains the
same. The FRM buys you stability at a premium.
It guards you against future interest rate shocks.
But it makes you vulnerable to that inflation
paradox if rates happen to drop dramatically.
You are paying for certainty. And that premium
protects you from the long -term risk of time.
But let's end with how the lender manages the
risk they take on. Right, because they don't
just sit there and pray that rates stay stable
for 30 years. Not at all. They use high finance
to neutralize the risk completely. And this is
the connection point that ties your home loan
directly to the global capital markets. When
a lender issues a massive portfolio of 30 -year
fixed -rate mortgages, they have a massive liability
on their books, a fixed rate in a potentially
volatile market. So how do they hedge that? They
sell off that fixed risk using financial engineering.
They engage in what is called a fixed -to -floating
swap, which is a type of derivative. Okay. What
does that mean in simple terms? Essentially,
the bank agrees to exchange the fixed stream
of interest payments they're receiving from you
for a variable or floating stream of payments
from a counterparty like a major investment firm.
So the lender keeps the stable payment stream
from the borrower, but then they use the derivative
market to trade that stability for a floating
rate. Why on earth would they want a floating
rate? Because if the central bank raises short
-term rates, the bank's own funding costs, what
they pay their depositors, also rise. By holding
a derivative that pays them a floating rate,
they receive more money when rates rise, which
perfectly offsets the higher cost of their funding
liabilities. So they transfer the fixed rate
risk to a specialist counterparty who is better
positioned to handle floating rates. They do.
It transforms the fixed -rate mortgage from a
simple loan contract into a piece of a much larger
global market designed to manage and distribute
risk. And I assume this requires some extremely
complex mathematics to price correctly. You have
to determine the value and risk of that rate
optionality? Oh, absolutely. This is where models
like the famous Black -Skulls equation, which
was originally designed for pricing stock options,
come into play in valuing and managing these
interest rate derivatives. They help the lender
assign a precise numerical value to the uncertainty
of future rate movements. So the next time you
look at your fixed monthly payment, remember
that it is the stable anchor of the... this massive,
sophisticated financial operation designed to
manage risk across decades, connecting your kitchen
table commitment to the deepest concepts of financial
mathematics and global markets. It's a number
engineered for certainty, but managed by speculation.
And that complexity is definitely worth exploring
further. We'll see you next time for the next
Deep Dive.