Pay off your mortgage early, or put your money to work elsewhere? In this article, we'll go through the math behind the question of whether it's better to pay off your mortgage sooner or to invest instead. Usually, when you're facing this question, it means you have some money left over after all your monthly expenses. And now you're just wondering how to best optimize these savings.
To figure out what's best for you, it will depend on a number of factors. The key one is the interest rate on your mortgage. But first, let's explain what a mortgage payment consists of, because understanding this mechanism is absolutely crucial to deciding what's right for you. Once we understand that, we can answer mathematically and financially what makes more sense.
How a Mortgage Payment Really Works
Okay, let's start from the very beginning. When you take out a mortgage, you're buying a house with borrowed money from a bank. You then have to pay it back with interest over time, because yes, that's how banks make money. Let's say you borrow 8 million CZK for a 10 million CZK house or apartment and take out a standard 30-year fixed-rate mortgage. The bank will simplify it for you and calculate how much you have to pay each month for the next 30 years, which is 360 payments.
Each monthly payment is broken down into two components:
- Principal – this is the part that pays down the amount you borrowed.
- Interest – this is the bank's reward for lending you the money.
For example, with an 8 million CZK loan over 30 years at 5% annual interest, the interest portion each month is calculated as remaining balance × 5% ÷ 12. The payment for such a mortgage is approximately 43,000 CZK.
And now comes the interesting part, or depending on how you see it, perhaps the slightly tricky part. A mortgage follows what's called an amortization schedule, also known as a payment schedule. This is a table that breaks down each payment—how much goes to interest and how much to principal.
In month number one, of that 43,000 CZK payment, approximately 33,500 CZK goes to interest and only about 9,500 CZK to principal. And that's exactly how mortgages work. The debt, the principal, barely moves at the beginning and only starts to decrease significantly much later in the life of the loan.
At first glance, this is a problem because interest accrues on your current balance, and when you're only chipping away at that balance slowly, the interest doesn't decrease much. It's so pronounced that in the first 16 years of a 30-year mortgage, you're still paying more in interest than in principal each month. In other words, for the first nearly 194 payments, most of the money goes to the bank, not toward paying off the debt itself.
If we look at the situation after 20 years (using the example of 8 million, 30 years, 5%), you will still owe roughly 4 million and 50,000 CZK. So, you're two-thirds of the way through the mortgage term, but you've only paid off about 50% of the principal, which is, admittedly, a bit unbalanced.
And the total amount paid? At 5% interest, you'll pay approximately 7.5 million CZK in interest. In total, you'll send the bank about 15.5 million. At a 3% rate, it's about 4,140,000 CZK in interest, for a total of around 12 million. I know, it's pretty staggering.
The takeaway is that if you reduce the principal as soon as possible, you not only shorten the repayment period but, more importantly, you reduce the total interest paid. You save a considerable amount of money in the long run. This makes a lot of sense, and you might be thinking, "No more information needed, I'm going to request an extra payment, right?" But not so fast, because this is where it starts to get interesting.
A Battle of Numbers: Paying Down vs. Investing
Let's take a look at market returns and see if it's mathematically better to pay down the mortgage or invest. When it comes to investing, the long-term average return of the S&P 500 index is historically around 10% per year. After accounting for fees, a realistic long-term expectation is around 8% per year. I'm using the S&P 500 as the most well-known representative of stock market indexes.
Now, let's imagine your mortgage interest rate is 3%. If you make extra payments on your mortgage, you're effectively earning 3% per year—that's how much less you'll pay in interest. But if you put that same amount into the stock market and earn 8% long-term, that's obviously more than three. So, purely mathematically, with a low rate, say 2.5% to 3%, investing comes out ahead of paying off your mortgage early.
But be careful, investing also has losing years, like 2018 or 2022. The risk of fluctuation is simply there. I'm not saying that should discourage you. As Warren Buffett says, volatility is the price you pay for a ticket to the markets.
My interim recommendation at this stage of the thought process: if you have a lower interest rate, say up to 3%, it will almost always be financially better to invest than to pay down your mortgage early. Once rates get to 6% or 7%, the decision is much closer. Some people might then prefer to pay it off early not for the math, but for the psychological benefit—the knowledge that they have a smaller mortgage.
But let's take our thinking one step further. Imagine a mortgage at 7%. Every extra payment at that point is a risk-free return of 7% per year. While that's not impossible in the market, it comes with risk. Not every year is positive, so the peace of mind and a guaranteed return can be reasons to pay it off sooner.
The Key Factor People Forget: Time and Compound Interest
However, and this part is the most important in my opinion, there's one more crucial factor we haven't talked about yet, and it's absolutely key to the whole equation: How many years do you have left on your mortgage and how many years until your goal (retirement or another milestone)?
Generally, the more time you have, the greater the potential advantage of investing, thanks to compound interest. I'd better say that again. Thanks to compound interest, which Albert Einstein himself called the eighth wonder of the world. Well, who knows if he actually said that or if he said it at all, but it's definitely a wonder.
For example: if you can put an extra 10,000 CZK per month to work and invest it for 25 years at 8% annually, you'll end up with roughly 9.5 million CZK.
If you put that 10,000 CZK per month toward extra mortgage payments (in the 8 million, 7%, 30-year model), you'll pay it off about 11 years earlier, so in approximately 19 years instead of 30, and you'll save about 4.5 million in interest.
You might say, "Okay, I paid off the mortgage 6 years earlier (compared to the 25-year investment horizon). So for those last six years after paying off the mortgage, if I put 10,000 CZK plus the entire original mortgage payment into investments, I must surely catch up to what I would have earned in 25 years in the first model."
But unfortunately, you won't reach the same amount. You'll have around 5.8 million CZK at the end of the 25-year period. So you still missed out on almost 4 million CZK.
I know, the comparison here is a bit unfair, because in one case there are still five years of mortgage payments left, and in the other, it's already paid off. However, even if we looked at the situation after 30 years, you would still be better off in the case where you set aside 10,000 CZK per month the entire time. The difference at the end would still be 2 million CZK after 30 years.
Notice that even though the numbers are very similar (8% return vs. 7% interest), your total wealth at the end comes out diametrically different. This is because a mortgage is governed by amortization (you save on future interest), while investments are governed by exponential growth (returns are credited continuously and then earn further interest). We are comparing different mechanisms, and that makes the comparison more complex than it might seem at first glance.
Over longer horizons, you can't just go by a simple subtraction of the mortgage interest rate from the expected investment return. This is very important to keep in mind.
Two Golden Rules and a Few Practical Tips to Conclude
You can use available calculators to figure out for yourself what such a calculation would look like for, say, a 3% mortgage. But don't forget to also consider that your payment on a three-percent mortgage will be significantly lower, leaving you with even more money to invest. And of course, not everyone has 25 years ahead of them. Maybe you have 5, 10, or 15 years to go. In that case, the battle between the two options might be much closer, but you need to calculate it precisely.
But remember two rules:
- The lower the interest rate on your mortgage, the more it pays to invest.
- The longer your time horizon, the more it pays to invest, even if the interest rate is high.
However, it's also important to add that we're talking about pure mathematics here. Paying off a house or apartment isn't always just a financial decision. The freedom of not having a mortgage payment can be more valuable than anything money can buy. So, I respect it when someone wants to pay off their mortgage as soon as possible. Even so, I think it's worth considering diverting some of the money you'd use for early repayment into investments and taking advantage of what I've described, at least partially.
It's also important to say that in the conditions of the Czech market, it's not practical to make an extra payment every month. The administrative costs could be so high that it wouldn't make sense. But that doesn't change the principles, and the same reasoning can be applied when deciding on the length of the mortgage term. It probably won't surprise you now that it makes sense to set up the mortgage for the longest possible term. The lower your payment, the more you can invest.
What do you think? Will you be more likely to pay off your mortgage early, or to invest?
