When you want to know how much your mortgage will be, there are several resources online that make it easy to get an estimate. Just search for “mortgage calculator” and you will find several sites with useful online calculators. Still, it is helpful to also know how your mortgage payment is calculated, in case you should need to check the calculations a loan officer gives you.
Calculators may or may not factor in private mortgage insurance (PMI). Not everyone will have to pay PMI, but if your down payment is less than 20%, or if you have a poor credit history, you should estimate from $80 to $150 per month, depending on the value of your home. A home valued around $160,000 will probably run you $80 in PMI every month.
To understand how mortgages are calculated, you should understand compound interest. It is the practice of calculating your monthly interest, adding it to the principle, and then recalculating interest for the next month on the new amount.
For a simple example, let’s look at borrowing money for one year with interest compounded monthly. If you borrowed $1,000 for one year at 5% compounded monthly, you would calculate it with this formula.
M = P * (i / (1 – (1 +i) ^ -N))
In the above formula, M is the monthly payment, P is the principle, i equals the monthly interest rate, ^ means to calculate to a given power, and N is the number of months. Notice we are calculating N to the negative power. You are probably used to seeing it displayed something like this: M = P * (i / (1 – ((1 +i)-N)). We use ^ because it is the symbol spreadsheets use to calculate exponential numbers.
So the easy part is figuring out P, our principle loan amount of $1,000. The monthly interest rate (i) is 5 percent divided by 12 months (.05/12) or .004167. N is simply 12 (12 months).
This translates our formula of M = P * (i / (1 – ((1 +i) ^ -N)) to a few steps. Calculate each section of the formula in the following order:
- 1+i = 1.004167
- (1+i)^-N = .951324
- 1-((1+i)^-N) = .048676
- i/(1-((1+i)^-N)) = .085608
You’ll need to pull out your trusty calculator to calculate the –N exponent. The final step is to multiply your result from the fourth step (above) by the principle. This gives you a monthly payment of $85.61…and that was a simple loan over 12 months!
Over the course of the year, you would apply your payment of $85.61 to the ending balance each month. You can see how the monthly interest is reduced each month because the principle is also reduced.
| Principle | Monthly Interest | Total |
1000.00 | 4.17 | 1004.17 |
918.56 | 3.83 | 922.39 |
836.78 | 3.49 | 840.27 |
754.66 | 3.14 | 757.80 |
672.19 | 2.80 | 675.00 |
589.39 | 2.46 | 591.84 |
506.24 | 2.11 | 508.34 |
422.74 | 1.76 | 424.50 |
338.89 | 1.41 | 340.30 |
254.7 | 1.06 | 255.76 |
170.15 | 0.71 | 170.86 |
85.25 | 0.36 | 85.61 – final payment |
Notice how most of the payment is principle in such a short-term loan. But when you stretch the same amount of money over ten years, you really get hit hard with interest. The one-year loan only costs you $27.29 over the life of the loan. Over ten years, it would cost you $272.66.
If you want to see the ten-year figures in action, you only need to change one factor in our calculations. Because N is the number of months, and the loan is for 10 years, N becomes 120 instead of 12. So now our formula of M = P * (i / (1 – ((1 +i) ^ -N)) breaks down to the following calculations:
- 1+i = 1.004167
- (1+i)^-N = .607137
- 1-((1+i)^-N) = .39286
- i/(1-((1+i)^-N)) = .010607
Now the monthly payment is a measly $10.61 but over the span of the loan, you pay almost ten times the interest, or $272.66. In the beginning, nearly half of the monthly payment goes towards interest.
Now that you understand how to calculate your mortgage payment, you need to add on the additional expenses discussed in the beginning of this article. Let’s take the example of a typical 30-year mortgage of $200,000 at an APR of 6%, compounded monthly as mortgages tend to be. Using our formula, we come to a monthly payment of $1,199.10.
If we only had 10 percent to put down, we must estimate another $90 per month for PMI. We then add on insurance, estimating about $50 per month. Finally, we need to consider taxes.
Taxes can vary wildly and may not even be based on the loan value of your house. Your best bet is to call the town where you live or where you are moving to and find out what the taxes would be. Let us say the tax rate is $12 per $1,000 of assessed value. If the town says the house is worth $150,000, then your taxes would be $1,800 per year or $150 per month. Your monthly payment works out this way.
| Monthly Mortgage Payment | $1,199.10 |
| PMI | $90.00 |
| Homeowner’s Insurance | $50.00 |
| Taxes | $150.00 |
| Total Monthly Mortgage Payment = | $1,489.10 |
But wait, after all of that work, we’re not done. Now you need to decide if you want to pay points. Generally speaking, on lengthy loans like a 30 year mortgage, points make sense only if you do not expect to refinance before your interest savings have paid for the cost of the points.
One point is assessed at 1 percent of the loan amount. On our $200,000 loan, a point would cost $2,000. Each point you pay reduces your interest rate by .125 percent. To find out the savings, you should figure out your monthly payment at the original rate, and then figure out the monthly payments at each point reduction. The difference, multiplied by the number of payments, will be the total savings.
In our scenario here, it would take about 125 payments to break even. As long as we are certain we will have the loan for at least ten years, it makes sense to buy as many points as we can afford. If we expect to refinance in the next ten years, points would be a waste of money.