# Demystifying How Mortgages Are Calculated

## The Importance of Knowing How to Calculate a Mortgage

• While there are plenty of mortgage calculators out there that do all the heavy lifting for you
• It can actually be helpful to know the math behind it
• You’ll probably better understand the implications of paying extra/early or the impact of a lower interest rate
• And if nothing else you can impress your friends and family

Mortgages can be complicated business – fortunately there are a ton of great calculators out there that take the legwork out of all the tricky math.

But as your teachers probably told you in school time and time again, it’s good to actually know how things work too. That’s why they asked you to show your work!

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. Well, probably not, but let’s move on.

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

## The Interest Part Is Easy to Calculate

• It’s very easy to calculate monthly mortgage interest
• A standard calculator will do the job if you need to run a quick calculation
• Simply multiply your loan amount by your interest rate and divide by 12
• That will give you the monthly interest due based on the outstanding principal balance

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.

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. No algebra required!

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 early. Funny how things change…

## How Do You Calculate the Entire Payment, Including Principal?

• The entire monthly payment formula is a bit more complex
• But you can still do it by hand if you’ve got nothing better to do
• Or are simply a math buff who wants to know how things work
• And perhaps more importantly why you’re paying the bank so much money!

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 and blow your mind.

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

And yes, it’s heavy on the algebra, real heavy for those of us not so thrilled with math. Warning: It’ll hurt your head.

## Here Is the Mortgage Formula

### 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

Still with me? 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, nothing ever is. This calculation above is only good for the very first payment based on the \$200,000 loan amount and a 30-year amortization schedule.

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.

Remember, each month on a fully-amortizing mortgage the balance goes down because a portion of the payment goes toward principal.

This is good news because it means you actually own more of your home each month instead of the bank.

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.

## In month two we calculate mortgage interest via the following formula:

\$199,685.24 x 0.035 / 12 = \$582.42

Instead of using the original \$200,000 loan amount, we need to account for that first principal payment made in month one.

The \$314.76 in principal lowers the outstanding balance to \$199,685.24.

If we multiply that amount by the same 3.5% interest rate and divide by 12, the total is \$582.42, which is the interest due for month two.

When we take our fixed total monthly payment amount of \$898.09 and subtract \$582.42, we come up with \$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.

In month three, you’d owe \$581.49 in interest and pay \$316.60 toward principal.

It’s the same \$898.09 you owe to your lender each month, but the composition of the payment changes.

## The Amount of Interest Due Dwindles Over Time

As time goes on, the interest portion of the mortgage payment falls, thanks to the smaller outstanding balance, and as a result the principal portion of the payment rises.

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

For example, in month 321 of our hypothetical home loan, you’d owe just \$98.76 in interest, with the remaining \$799.33 going toward the outstanding balance.

Remember, the total payment amount on a fixed-rate mortgage doesn’t change for the entire 360 months (or 180 months if it’s a 15-year fixed).

But how your payment is allocated does change over time.

Knowing this can help you better understand your mortgage and perhaps dictate decisions when it comes to a possible refinance.

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 to know how it is calculated, but way too much work. And you should be spending your free time doing something a lot more fun.

Read more: Are mortgage calculators actually accurate?

(photo: Jorge Franganillo)