# How are mortgage payments decided? [duplicate]

I always used to think that monthly mortgage payments had fixed proportion of interest payments and house payments (determined by rate and term). But, I recently heard that you start off with making most of your payments on interest and slowly more of it becomes house payment.

Why is this so? Is it to force people to stick to their mortgage? And, is there a method to calculate the proportions over time?

Any help would be appreciated. Thanks!

It's easiest to get your payment from the `PMT` function in Excel or Google Sheets. So a \$100,000 30 year mortgage at 3% looks like this:

``````=PMT(0.03/12,360,100000)
``````

The basic calculation is pretty simple. You take the annual interest rate, say 3%, divided by 12, times the existing principal balance:

``````Month   Principal  Interest  Payment
1    100,000.00  250.00  -421.60
2     99,828.40  249.57  -421.60
3     99,656.37  249.14  -421.60
4     99,483.91  248.71  -421.60
5     99,311.02  248.28  -421.60
6     99,137.70  247.84  -421.60
7     98,963.94  247.41  -421.60
8     98,789.75  246.97  -421.60
9     98,615.13  246.54  -421.60

....and then .........

111     78,304.34  195.76  -421.60
112     78,078.50  195.20  -421.60
113     77,852.10  194.63  -421.60
114     77,625.13  194.06  -421.60
115     77,397.59  193.49  -421.60
116     77,169.49  192.92  -421.60

...... but then ......

339      9,016.01   22.54  -421.60
340      8,616.95   21.54  -421.60
341      8,216.90   20.54  -421.60
342      7,815.84   19.54  -421.60
343      7,413.78   18.53  -421.60
344      7,010.71   17.53  -421.60
345      6,606.64   16.52  -421.60

etc.
``````

The idea is that borrowers would like to have a predictable payment. The earlier payments are proportionally more interest than principal than later payments are but that's because there is much more principal outstanding on month 1 than on month 200.

• So they use a series summation formula to derive the derive the magical monthly payment that everyone needs. – user2999870 Aug 17 '17 at 7:00
• @user2999870 It isn't very magical, at the beginning of a mortgage you have more debt, so the monthly interest charged is higher (the payment is constant, so the amount going to principal must be lower), at the tail end you have a small debt, so you have a small amount of monthly interest, which means your payment must be going mostly to principal. – Paul Aug 18 '17 at 2:29

It's so that your total mortgage payment stays the same every month. Obviously, the interest due each month decreases over time, as part of the principal is paid off each month, and so if the proportion of interest and principal repayments were to stay the same then your first payment would be very large and your last payment would be almost nothing.

• Oh I see. I had the misconception that mortgages use the compound formula that they've been teaching in high school for ages. I've seen how the formula is derived and its pretty intuitive. – user2999870 Aug 17 '17 at 7:02
• @user2999870 Can you edit the question to include the formula to which you refer. – Mike Scott Aug 17 '17 at 7:04
• Well, I got what I wanted. I thought p(1+r/n)^nt was used but I was mistaken. – user2999870 Aug 19 '17 at 4:20

It has nothing to do with forcing people to pay off their debt; in that case it would make better sense to have people pay off debt rather than interest.

It is because you want to have your actual payment stay the same each month, which is easier for the vast majority of people to comprehend and put into their budget. It is called an annuity in Finance terms. In theory you could use another method - eg. pay of the same amount of debt each month - then your interest payments will decrease over time. But in that case your monthly payment (debt + interest) will not be stable - It will start of high and decrease a little bit each month. With an annuity you have a constant cashflow.

In Finance you generally operate with three methods of debt repayment:

1. Annuity: Fixed cashflow. High interest payment in the beginning with small debt payments - later it will be reversed.

2. Serial loan: Fixed debt payments. Debt payments are equally spread out accross the period - interst is paid on the remaining debt. Cash flow will decrease over time, because interest payments become smaller for each period.

3. Standing loan: You only pay interest on the loan, no debt payments during the period. All debt is payed back in the end of the loan.

In Europe it is common practise to combine a 30 year annuity with a 10 year standing loan, so that you only pay interest on the loan for the first 10 years, thereafter you start paying back the debt and interest, the fixed amount each month (the annuity). This is especially common for first-time buyers, since they usually have smaller salaries early in life than later and therefore need the additional free cash in the beginning of their adult life.