How much your monthly mortgage payment will total can be a big mystery, especially for the first-time homebuyer. But a quick bit of math will supply the answer. Don’t worry, it’s easier than it looks. Here’s how to calculate your monthly mortgage payments on a fixed-rate loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
The variables are as follows:
- M = monthly mortgage payment
- P = the principal, or the initial amount you borrowed.
- i = your monthly interest rate. Your lender likely lists interest rates as an annual figure, so you’ll need to divide by 12, for each month of the year. So, if your rate is 5%, then the monthly rate will look like this: 0.05/12 = 0.004167.
- n = the number of payments, or the payment period in months. If you take out a 30-year fixed rate mortgage, this means: n = 30 years x 12 months per year, or 360 payments.
The longer the loan, the less you’ll pay each month. You will, however, also pay more in total, because interest compounds. Essentially, you’ll be paying interest on interest. So you multiply the interest rate by itself for each term of payment — hence the exponent in the formula. That will have a great bearing on your decision between a 30-year fixed-rate and a 15-year. Let’s compare.
Say you’ve decided to buy a home that’s appraised at $500,000, so you take out a $400,000 loan with an interest rate of 3.5%. Let’s take a look at the 30-year loan. For quick reference, again, the formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Our P, or principal, is $400,000.
Remember, with i, we must take the annual interest rate given to us — 3.5%, or 0.035 — and divide by 12, the number of months in a year. This calculation leaves us with 0.002917, or i.
Our n, again, is the number of payments. And with one payment every month for 30 years, we multiply 30 by 12 to find n = 360.
When all is said and done, we learn that, for a 30-year loan at 3.5% interest, we’ll pay $1,796.18 each month.
For the 15-year loan, the math is nearly identical. All that’s different is the value of n. Our loan is half the length, and so n is 180. Each month, then, we’ll pay $2,859.53, over 60% more than with the 30-year loan.
Over time, though, the 15-year loan is a far better deal, as interest compounds. You pay $514,715 over that time. With the 30-year, you pay $646,624 — over $100,000 more.
Your decision between these two, quite simply, hinges on whether or not you can float the significantly higher monthly payments for a 15-year loan.
How can I lower my monthly payment?
You can lower your monthly payment in a few ways:
- Increase the term of the loan. As shown above, the longer you take to pay off the loan, the smaller each monthly payment will be. The downside is that you’ll pay more interest.
- Decrease the size of the loan. Of course, if you have a smaller loan balance to begin with, you’ll need to fork over less each month to pay it off.
- Get to the point where you can cancel your mortgage insurance. Some lenders require you to buy mortgage insurance if you put less than 20% down. This is another charge that gets added to your monthly mortgage payment. You can usually cancel mortgage insurance when the ratio of your remaining balance to the home value is less than 80%.
- Look for a lower interest rate. You can think about refinancing (if you already have a loan) or shop around for other loan offers to make sure you’re getting the lowest interest rate possible.
Can my monthly payment go up?
Your monthly payment can rise, in a few cases:
- You have an adjustable-rate mortgage in which your payment stays the same for an initial term (such as 5, 7 or 10 years) and then readjusts every year.
- If you have an escrow account to pay for property taxes or homeowner’s insurance, those taxes or insurance premiums may increase. Your monthly payment includes the amount paid into escrow, so the taxes and premiums affect the amount you pay each month.
- You may have been assessed fees. Check your mortgage statement or call your lender.
A little math can go a long way in providing an affordability reality check.