So you've come across the perfect home and you want to know if you will be able to afford the payments. You can use our mortgage calculators to get an idea how much will be your monthly mortgage payment. But it is still a good idea to understand how mortgage payments are calculated, should you need to confirm the figures you are getting from a loan officer.
Mortgages run on compound interest, the practice of applying the interest rate and adding that value to the balance of the loan. The next month, interest will be calculated on the new amount.
To put it more plainly, if Mary deposits $1,000 in a savings account, earning 2% interest yearly, at the end of the year, she will have $1,020. If she leaves the money there, the following year the interest will be calculated based on the new $1,020 balance. This time, she will earn $20.40 and that will be added to the balance for a total of $1,040.40. The interest she earns will keep increasing each year.
How Mortgages Work
In the case of mortgages, compound interest is calculated in the same way, except your balance is reduced by your monthly payments. So, even though the interest has increased your loan balance, your payment has then brought the balance down lower than the previous month. Therefore, each month your total cost of interest goes down and more of your payment goes towards the principle. You begin the mortgage paying only a fraction of the principle and make your final payments with only a small portion goings towards interest.
Calculate Your Monthly Mortgage Payment
The formula for calculating what your payment will be is as follows:
M = P * (i / (1 - (1 +i) ^ -N))
Don't let your math anxiety get the best of you. Going through the formula step by step will simplify the process. You can always use our Mortgage Calculators
Each of the letters in the formula represents a figure in your mortgage. M stands for monthly payment. P is the Principal or amount borrowed. The i stands for your monthly interest rate, or your yearly rate divided by 12. N is the number of months in the loan. The ^ symbol represents calculating the -N power. This symbol is used in spreadsheets for that function. Even if you feel lost right now, following the next steps will simplify the equation.
The easiest part is figuring for P, our principal loan amount of $200,000. At a rate of 5 percent, the monthly rate works out to .004167. N is just the number of months. On a 30-year loan, there are 360 months.
Replacing the letters with numbers, we get:
M = $200,000 * (.004167 / (1 - (1 + .004167) ^ -360))
Do the math one section at a time starting inside the parentheses using a calculator as follows:
(1+ i) = 1.004167
(1+ i)^-N = .223827
(1-(1+ i)^-N)) = .776173
(i/(1-(1+ i)^-N)) = .005368
Finally, multiply the fourth number above (.005368) by the Principal to find your monthly payment. In this case, it is $1,073.64.
So if Mary can afford $1,073.64, that's a good thing, but she still has more work to do. She needs to add in personal mortgage insurance (PMI) if it applies to her situation. If she has only 10% to put down on the house, she'll end up paying about $90 a month in PMI. She will also have to pay taxes and homeowners insurance.
Taxes rates vary from town to town. Before making a decision, call the town or go online to find out the amount of taxes the homeowner paid on the house last year. Diving the amount by 12 and add to your monthly cost. Estimating $300 per month to cover taxes and insurance should be sufficient for our work here.
Monthly Payment (on $180,000) $966.27
Homeowner's Insurance $50.00
Total Monthly Payment = $1,356.27
Even then, we've got one more step to go through. Mary needs to look at paying points and decide if it is worth the cost to get a lower interest rate. One point costs 1 percent of the loan principal. On Mary's $180,000 loan (remember she put 10% down), one point costs $1,800 and brings the interest rate down by .125 percent. If Mary can afford two points at a cost of $3,600, it will bring the interest rate down to 4.75%, resulting in a monthly savings of only about $30. In about ten years, that $360 per year savings will add up to her investment. Over the life of the loan, she will save a total of $6,232.94.