Demystifying How Mortgages Are Calculated

how are mortgages calculated

Mortgages can be complicated business – fortunately, there are tons of great calculators out there that take the legwork out of trying to do all the tricky math.

But as your teachers probably told you in school, it’s good to actually know how things work too.

And hey, it’s never smart to rely too heavily on technology in case something goes wrong. Oh, and you can impress your friends too.

That brings us to how mortgage interest works. Ready to do some algebra? Neither am I, but let’s try it anyways.

Let’s say you’ve got a 30-year fixed mortgage with a loan amount of $200,000 and your mortgage rate is 3.5%. Fairly common scenario these days.

The Interest Part Is Easy

A simple way to determine how much your interest payment is each month is to multiple your loan amount by the interest rate, and then divide by 12.

$200,000 x 0.035 / 12= $583.33

So in the scenario above, we’d come up with $583.33. This would be the interest portion of your monthly mortgage payment. Pretty basic stuff here.

And hey, had this article been written back in 2006, we’d be done because most people held interest-only loans and didn’t even make principal payments.

But times have changed, and now everyone wants to pay off their mortgages .

How Do You Calculate the Entire Payment, Including Principal?

Most people probably don’t care nor want to know this second part, but I figured I’d share just to cover all the bases.

If you want to calculate your entire mortgage payment. including both the principal and interest portion, you need to use the formula below.

And yes, it’s heavy on the algebra, real heavy for those of us not so thrilled with math.

P = L[c(1 + c) n]/[(1 + c) n – 1]

P= monthly payment

L = loan amount = $200,000

C = periodic interest rate = 0.002917 (3.5%/12 months)

N = number of payments =

360 (30 years)

Lost yet? Don’t worry; I won’t make you do the math. Heck, I used an algebraic calculator to come up with the answer.

Let’s break it down:

P = 200,000[0.002917(1.002917)^360]/ [(1.002917)^360-1]

P = 200,000 x 0.00449045

P = $898.09

Phew. So the total monthly mortgage payment is $898.09. And because we know the interest portion already ($583.33), the principal portion of the payment must be $314.76.

Of course, it’s not that simple. This calculation above is only good for the very first payment based on the $200,000 loan amount.

When calculating the following month’s payment, you would have you use the new loan balance, which falls to $199,685.24 thanks to that $314.76 principal payment.

Fortunately, we already know the total payment amount, which is fixed for the full loan term. so we can just calculate interest and then the rest must be principal.

So in month two, we calculate interest by doing the following:

$199,685.24 x 0.035 / 12 = $582.42

Taking our total monthly payment amount of $898.09 and subtracting $582.42, we come up with the $315.67, which is the second principal payment.

As you can see, the interest portion of the payment dropped slightly, while the principal portion increased.

Over time, the interest portion of the mortgage payment falls, thanks to the smaller outstanding balance, and the principal portion of the payment rises.

In fact, at the end of the loan term, assuming you don’t refinance or prepay, the interest portion will account for just a few bucks of the total payment.

However, the total payment amount doesn’t change. It’s just how your payment is allocated over time that changes.

I’ve probably confused more people than intended here, but it’s always good to know how things work, even if you don’t actually do the math yourself.

For the record, I recommend using a mortgage calculator as opposed to trying to do all this math by hand. It’s interesting, but way too much work.


Category: Credit

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