Finding the interest paid, principal reduction, and new balance after a mortgage payment

Three-part: interest portion = balance × (r/12), principal reduction = monthly payment − interest, new balance = balance − principal reduction.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Diane's mortgage v1

On January 1, the home mortgage balance was $215,000 for the home owned by Diane. The interest rate for the loan is 6 percent.

Assuming that Diane makes the January monthly mortgage payment of $1,400, calculate the following:

(a) The amount of interest included in the January payment.
(b) The amount of the monthly mortgage payment that will be used to reduce the principal balance.
(c) The new balance after Diane makes this monthly mortgage payment.

Hank's mortgage v2

Hank's mortgage balance is $184,500 at 7.2%. His monthly payment is $1,290.

(a) Interest portion of this payment.
(b) Principal reduction.
(c) New balance.

Reina's mortgage v3

Reina's mortgage balance is $320,000 at 5.4%. Her monthly payment is $1,795.

(a) Interest portion.
(b) Principal reduction.
(c) New balance.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 How to Solve It

Diane's $1,400 payment splits into $1,075 of interest and just $325 of principal. Classic mortgage shape — early payments are mostly rent on the balance.

interest portion = balance × (r/12)
principal reduction = M − interest
new balance = balance − principal reduction

Three lines, applied to one specific payment. Apply 360 times for a 30-year amortization schedule.

Compute the interest portion (part a).

The bank charges this month's interest on the current balance. r/12 = 0.06/12 = 0.005.

interest = 215,000 \times 0.005 = $1,075.00

Compute the principal reduction (part b).

Whatever's left of M after interest pays down principal.

principal = 1,400.00 - 1,075.00 = $325.00

Compute the new balance (part c).

Old balance minus the principal reduction. The interest doesn't reduce the balance — only the principal portion does.

new balance = 215,000 - 325 = $214,675

Diane just paid $1,400 but only $325 went to building equity. 76.8% of her payment was interest. That's mortgages.

▸ COMMON SLIPS(1) Used the full monthly as interest. Only the interest portion is interest. (2) Subtracted M from the balance. The interest gets paid to the bank, not subtracted from the balance. Only the principal reduction lowers the balance. (3) Used the annual rate. Always use r/12 for monthly arithmetic.

04 Practice — Step by Step

Try Hank's mortgage. Same three steps.

Compute the interest portion.

Hank's balance is $184,500 at 7.2% APR. What's the interest portion of this month's payment?

interest = $

Compute the principal reduction.

Hank's monthly payment is $1,290; interest is $1,107.00 (from step 1). How much of the payment goes to principal?

principal = $

Compute the new balance.

Old balance $184,500; principal reduction $183. What's the new balance after this payment?

new balance = $

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Q4 Q6