# How to Calculate a Mortgage Payment

I’d like to go about showing you how you would calculate a mortgage payment. so we have a really nifty formula that we can use, where we just say the payment, right. So the monthly payment that’s due your mortgage payment is going to be equal to the principal that’s how much money you’re borrowing, right.

So if you’re borrowing 120 thousand dollars that’s your principal and you’re going to multiply it by this fraction right here. So in the numerator and the top of this fraction, we’ve got R and so this R it’s actually going to show up several times. This R is actually the interest rate that you’re paying.

So the APR the annual interest rate. We have to divide that by 12, why because we’re making monthly payments, right. So we take R we took the interest rate divided by 12 take that r we multiply it by 1 plus R to the nth power, that n is an exponent, right.

Now that n also represent something that is the number of payments that you’re going to be making. So for a 30-year loan there’s 12 months in a year and if you make a payment every year so you’re gonna have you’re gonna have 30 years times 12 right. 12 months in a year, 30 years that’s going to tell you how many payments you have to make. So that would be 360, right. If you were doing a 30-year loan,right.

If you’re doing a 15 year loan it’d be 30 or excuse me 15 times 12 would be 180 and then a denominator does have that 1 plus R to the nth power and then we subtract 1. So if we follow this this formula here, that’s going to yield our monthly mortgage payment, right, and now when I’m we’re not to kind of simplify things we’re not going to think about property taxes or other things that might be lumped in with the mortgage payment.

We’re just going to think about repaying the principal in the interest right now. Just so you can get a feel for how that you would go about calculating this for a mortgage. So let’s say that you borrow \$100,000 at six point five percent APR, right. To be repaid over 30 years, so you’ve got a 30-year mortgage.

Now we want to say what would be the monthly payment and we want to calculate the monthly payment so we know how much to pay the lender each month, right. So our monthly payment it’s going to be equal to our principal, right, and our principal is \$100,000.

That’s how much money we’re borrowing and now we’re going to multiply that by this fraction above, right. But we need to know what R is. So we’re going to have point zero six five divided by 12 that’s our R. If you remember our interest rate divided by 12 . This number we can just put it I’m just going to put in here, so you can see it and so forth.

But you really want to know it comes out and I’ll just round it point zero zero five four one seven that’s rounded but I’m just going to leave it in here like this, all right. So you can see then we add or excuse me x one plus R which is point zero six five over 12 and then we raise that to the nth power, right, and the nth power since it’s a 30-year mortgage there’s going to be we’re going to have 30 times 12 360 payments, all right.

So this is going to be to the three hundred and sixtieth power okay. now in our denominator the bottom part of our fraction and change colors here again. We’re going to have one plus point oh point zero six five divided by 12 to the three hundred and sixtieth power, that’s that n again and then we’re going to subtract one, right.

So you can put this into Excel or if you have a graphing calculator you’ll be put it in and you just take the hundred thousand and then you multiply it by this big fraction right here. Okay that is going to yield believe, we are going to have a monthly payment of 632 dollars.

So we’re gonna have a monthly payment of 632 dollars, that’s going to be our monthly mortgage payment and again just to just a note here, you’re paying this on a monthly basis but there might be other things right such as property tax, homeowners insurance, that the lender decides, you know.

What we’re going to put that we’re going to put it at in as part of the loan that’s part of your mortgage payment. We’re not getting into that here, we’re just talking about repaying this principal along with this six point five percent interest over a 30-year term and to do that you’d pay six hundred and thirty-two dollars a month for 30 years.