How to calculate Mortage Payments

Interest Rates. Principal. Terms. Amortization. Down Payment. Fixed/Variable Rates. All these terms can add up to be a confusing mix of what makes a mortgage payment. Most of us would just plug these numbers into a mortgage calculator to figure out approximately how much we’ll need to pay monthly (or whatever your payment frequency is). But have you ever wonder how the end payment number is calculated? Wonder no more. Keep reading to find a simple way in calculating your own mortgage payments and being prepared to plan your finances.

Time Value of Money

Before we can talk about how mortgage payments are calculated, we should first ask why. Why are we paying more for the money we borrowed? Well that’s simple, because of interest rates. But why are there interest rates in the first place? Bear with me as I get a bit philosophical. The concept of “time value of money” is commonly understood in finance as that a dollar today is worth more than a dollar in the future. Similarly, a dollar today is worth less than a dollar in the past. The latter can be easily understood with an example. The price of a bottle of Coca-Cola (Coke) cost 5 cents in 1886. The remained that way for 70 years, but could not keep up the same price past the 1940s. Costs of ingredients rose (inflation) and it ended up costing the company way too much money. A can of coke can go for about $1.50 today. That’s 30x the price! Here’s a great article on the topic.

So now that we understand that money isn’t as valuable in the future as it is in the current date due to inflation, we can look into how interest is used to help combat inflation. If you were to invest $1000 in an interest bearing vehicle like a bond at say 5%, the return will be $50 in a year. That can help protect your $1000 against the creep of inflation so you still have the ability to buy the same amount of cokes (keeping the same purchasing power). Similarly, when a bank lends you a mortgage loan, they’d like to protect their loan against inflation (and perhaps earn a little profit) by charging you an interest rate along with the loan. These rates can come as either a fixed rate or a variable rate. For more information about the differences, check out this detailed breakdown. For the purposes of simplicity, we’ll be using fixed rates to calculate mortgage payments.

The Formula

Mortgage Payment = P [ i * (1 + i)ⁿ ] / [ (1 + i)ⁿ – 1]

P = principal loan amount

i = monthly interest rate

n = number of months required to repay the loan