Home mortgages are based on the concept of monthly interest, but with a compounding effect. You take out a loan for a certain amount of money, at a specific interest rate and duration. The lender is then able to run those numbers through a formula that tells you the required monthly payment based on the principal, interest rate, and length of the loan.
When you go to buy a home, you typically know how much you are willing to spend and how much money you have to put down. The common mortgage durations are 15-year and 30-year, and the bank will tell you what interest rates they have available for each of those loan types. The mortgage broker will plug these values into a calculator, which will spit out a monthly payment amount. Check out my previous post for a refresher on mortgage concepts.
Ever wonder how they come up with that number for the monthly payment? Well, here is the formula and an example with a $200,000 mortgage for 30 years at 4.5% interest:
That’s an ugly formula, but thankfully, we have a simple Excel calculation that will handle this for us.
=PMT(Periodic Interest Rate, Periods, Loan Amount)
The Periodic Interest Rate is basically the annual interest rate on the mortgage divided by 12 to gain a monthly interest rate. The number of periods is the number of years for the mortgage multiplied by 12.
This is an easy way to model various scenarios to see what impact different interest rates or loan amounts have on your monthly payment.
How much am I really paying against the principal each month?
It depends on how many payments you have already made against the loan and if you have made any additional payments against the principal. Here is a graph that shows the percentage of your mortgage payment that goes towards the principal over the course of a 30-year mortgage:
In order to understand the details behind this, we will need to delve into the amortization table.
Understanding the Amortization Table
Let’s think about your mortgage in a different way. Imagine it is a board game with 360 squares. The goal of the game is to reach the end of the board. If you move a single square each month, essentially paying your required payment, in 30 years you will reach the end of the board and the jackpot of a fully paid off home.
Now, let’s extend this idea and add a value to each square. This value is the remaining balance on the loan. At the beginning, the remaining balance is the full amount of the loan and at the end the remaining balance is $0. The value of the remaining balance in each square is essentially the original loan amount, minus the total amount you have paid down against the principal.
In this version of the game, you can move ahead as many squares as you want each month. The only catch is you have to pay extra on your monthly payment to get your remaining balance down to the value of the square you want to move to.
The game board for this game is the amortization table. It’s really just a straight list, you can only move forward. There are no forks, branches, or detours. There is no going back, unless you start missing payments. Let’s assume that you are at least making the required monthly payments.
You most likely have a copy of the amortization table as part of your loan paperwork. If not, there are calculators like BankRate that can provide you with an amortization table based on your loan information. You can also build one in Excel if you want to get all DIY on it. I noticed that the latest version of Microsoft Excel even has a default template with a mortgage calculator, that will give you an amortization table tab.
How is the amortization table built?
The first step is to determine the amount of the monthly payment, using the formula from earlier in this post.
Let’s use the example where we have a $200,000 mortgage at 4.5% interest, with a monthly payment of $1,013.37.
In the first month of the loan, we have a remaining balance of $200,000. For that month, we will pay .375% interest. This is our annual interest rate of 4.5% divided by 12. That means we take $200,000 * .00375 which equals $750. If our monthly payment is $1,013.37 and we have to pay $750 in interest, that leaves $263.37 that goes against the principal.
In month two, we have a remaining balance of $199,736.63. If we do the same calculation, multiplying it by .00375 which is our monthly interest rate, we see that in month two we only need to pay $749.01 in interest. That is $.99 less than in the first month and it means that extra $.99 goes against our principal. This is because the monthly payment is fixed, it does not change based on how much of the principal remains to be paid.
What’s on the Amortization Table?
The amortization table consists of a few major fields:
Payment Number – This is just the number of the payment between 1 and either 180 or 360 depending on the duration of the loan, 15-year or 30-year.
Payment Date – This is the date the payment is due. It allows you to find a particular point in time and see how much you will owe on that date.
Opening Balance – The balance prior to making the monthly payment. This is the amount the interest portion of the payment will be based on.
Interest Payment – The amount of the mortgage payment that will go towards interest.
Principal Payment – The amount of the mortgage payment that will go towards the principal
Ending Balance – This is the remaining balance after the payment for the month has been processed. The ending balance for a particular month becomes the opening balance for the next month.
The Compounding Effect in the Amortization Table
At the start of the post, I mentioned that there is a compounding effect. Let’s dig into that a bit more.
From the perspective of each month, the interest you pay for that month is simple interest. It is 1/12ththe annual interest rate multiplied by the remaining balance. That means that each month, the amount of money being paid in interest is going down, but the payment is staying the same. This in turn means that the amount paid against the principal is getting larger each month. This is the compounding effect that over time accelerates the amount of principal paid in each payment over the previous one, which we saw in the earlier graph.
Consider this, if you pay $5,000 extra against the principal in the first month of the $200,000 30-year mortgage, you will cut 18 months off your mortgage.
What if you just pay your normal payment each month for the first 5 years of the mortgage. Then you get a bonus at work and make that $5,000 pre-payment against your mortgage in the 61st month? You will only end up cutting 14 months off your mortgage.
Why is it that the $5,000 pre-payment against the principal made at different points in the mortgage reduced the total time remaining by different amounts?
Let’s look at a graph of the remaining balance of the loan month by month. To easily identify the point at which half the loan is paid off, I’ve added an Equity curve. The equity curve is just the total amount paid against principal. If you have 30% of the loan remaining, you have equity equal to 70% of the original loan amount.
There are a couple of very interesting points to make from this graph.
The equity curve intersects with the remaining balance curve at month 240. That means that you will have paid off half of your mortgage principal after 20 years.
The rate at which the remaining balance decreases gets faster over time. This is because each month the interest due is calculated against the remaining balance, which goes down every month because of the principal payment. The mortgage payment stays the same, so that means after the interest is paid, there is more money available to go against the principal. This has a compounding effect. In fact, the amount by which the principal payment increases is just slightly less than the monthly interest rate.
That equity curve has a very familiar look to it. In fact, it looks like the investment curve from this post on compounding interest. Let’s do a quick Excel calculation.
If I take the principal portion of my first payment $263.37 and use that as a monthly payment amount, invested for 30 years, at 4.5% annual return, how much do I have after 30 years.
=FV(.045/12, 360, -263.37) = $199,999.53
That is 100% of the original balance on the loan.
Let’s look at a couple other intersections on the graph.
The first is the breakeven line that is set at 8.5%. This is based on the idea that if you buy a home with 20% down, you need to pay down the mortgage by 7.5% to be able to sell the house using a standard 6% realtor and still retain your original down payment, essentially breaking even. I added an additional 1% because of other costs like closing costs or mortgage origination fees, but this could be a bit conservative. That means the 8.5% breakeven line may be around 9.5% depending on your particular details.
Based on making the required monthly mortgage payment, you will have paid off enough to break even in month 58 at 8.5% or in month 64 at 9.5%. This is why it is normally recommended to not buy a house unless you plan to stay there for at least 5 years, because if you sell before then, you will lose some of your original down payment
The next line that is important to understand is the red curve, which represents the percent of the total interest paid. This means that 10 years into the loan, you have already paid 50% of the total interest on the loan. At this point, you have only paid off 20% of your actual principal. This is why at 10 years banks are looking to refinance your loan.
At the 20-year mark, you are now done paying off 50% of the principal for the mortgage, but the bank has now collected 85% of the total interest.
Key Takeaways:
- Make pre-payments earlier in the term of the loan to take more time off the total loan duration for the same amount of pre-payment.
- The faster you can move down the amortization table, the more money from each payment that goes against principal. This means more money you actually get to keep in the long run. After all, you get the money back that you paid against principal if you sell your home, interest is lost forever.
- Monthly interest for a traditional mortgage payment is only calculated once per month. Paying multiple times each month does not help. (Unless you have a simple interest loan, which is usually not recommended.)
Disclaimer: I am not a tax accountant, financial advisor, or lawyer. The information provided is based on how I analyze these investments and my own personal experience. I make no guarantees or predictions about the future performance of the markets, economy or interest rates.
Mortgage Concepts – Breaking Down The Home Mortgage – Part 1
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