How to figure interest on mortgage loans

[an error occurred while processing this directive]With a mortgage you pay interest every month on the entire unpaid balance. Here's how it works.

Let's say you borrowed $100,000 to buy a house at a high interest rate, of 9%, for 30 years. To find the interest we owe for the first month, first we take 9% of the $100,000 balance, which is $9,000. Then we divide by 12 because there are 12 months in a year and you're paying interest only for that month. So $9,000 ÷ 12 = $750. That's how much interest you pay in the first month. The total payment on your loan is $805, so $750 goes towards interest, and only $55 goes towards principal -- meaning only $55 goes towards paying back the $100,000 you borrowed.

Since you paid down your principal balance by a whopping $55, when the next month comes around you owe interest only on $99,945. Your interest in the second month is $99,945 x 9% ÷ 12 = $750. So again, $750 goes to interest, and $55 goes to principal. Actually, you pay slightly less interest than the previous month, but you don't see it because we rounded off the pennies. Here's how it looks without rounding.

Paying down a $100k, 30-year mortgage @ 9% (Monthly pmt. = $805)

Month

Principal
Balance

Interest Paid
(Principal x
9%/12mos.)

Principal Paid Down
(Monthly Payment
less Interest paid)

Percent of payment
going to interest

1

$100,000.00

$750.00

$55.00

93.2%

2

99,945.00

749.59

55.41

93.1%

3

99,889,50

749.17

55.83

93.1%

4

99,833.67

748.75

56.41

93.0%

That's certainly depressing. After four monthly payments of $805, you've paid $3,220 total, but you've only paid down your loan by $222.65!

The only good part of this is that as time goes on, more and more of your payment goes to principal and less and less goes to interest. But most of your payment will still go to interest for a very long time. Here's what it looks like in graphical form, with a lower interest rate than the example above.

Percent of monthly payment that goes to interest, by year

30-year loan @ 7%

Notice that in year 15 when you're halfway through the term, 75% of each payment is just going to make the bank richer, and only one-fourth is actually paying down your balance and building equity. Ouch! You have to get all the way to year 22 before more of your payment goes towards principal than towards interest.

Here's the same concept, looked at from the other end.

Equity built by year

30-year loan @ 7%

After 15 years you don't own half your home. You own only about 25% of it. You don't own half of it until about year 22.

Is there any way to get a better deal? Yes, there are two ways. Getting a 15-year loan, or making prepayments. So, moving on....

 

15-year loans save a bunch of interest

One way to save on interest is to get a mortgage with a 15-year term instead of a 30-year term. Here's how the loan we first looked at above would work at 15 years.

Paying down a $100k, 15-year mortgage @ 9% (Monthly pmt. = $1014)

Month

Principal
Balance

Interest Paid
(Principal x
9%/12mos.)

Principal Paid Down
(Monthly Payment
less Interest paid)

Percent of payment
going to interest

1

$100,000.00

$750.00

$264.00

74.0%

2

99,736.00

748.02

265.98

73.8%

3

99,470,02

746.03

267.97

73.6%

4

99,202.05

744.02

265.98

73.4%

The monthly payment on a 15-year mortgage is higher than for a 30-year mortgage, and the extra money pays the principal down faster. Since your outstanding debt is shrinking faster, there's not as much debt each month to pay interest on, so you pay much less interest over the term of the loan. The lesson here is that you want to get a 15-year term, not 30, if you can afford it.

Here's a calculator showing the difference.

Loan amount

Interest rate

%

15-year
30-year

Monthly Payment
$
$

Total Paid
$
$

Total Interest Paid
$
$

Extra interest paid
  on a 30 vs. a 15
$

 

Making prepayments

You might not be able to get a 15-year mortgage, since the payments are higher. Or you might already have a house with a 30-year mortgage. In these cases, if you can afford it, just make extra payments on your principal each month. Whether you're paying by check or online, there's usually a blank to write in how much extra principal you want to pay. (If not then contact the bank and ask them how to prepay.) Just make sure that your mortgage agreement doesn't contain a prepayment penalty clause. (Most don't.)

How much should you prepay? We cover that in our separate article about how to make prepayments.

 

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