MAT-144 · Mathematical Reasoning Topic 04 · Loans
Topic 04 · Review · Q5

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 Worked Example Video

Every step of Finding the interest paid, principal reduction, and new balance after a mortgage payment explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
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

On January 1, Diane’s mortgage balance is $215,000 at 6% APR. Her January monthly payment is $1,400.

What’s the new balance after Diane makes the January payment? Type just the number.

new balance = $
Hank's mortgage

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

What’s the new balance after this month’s payment? Type just the number.

new balance = $
Reina's mortgage

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

What’s the new balance after this month’s payment? Type just the number.

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 The Rule
interest portion = balance × (r/12) the “rent” on the balance
principal reduction = M − interest then new balance = balance − reduction
Three arithmetic lines, one specific payment. Every mortgage payment splits into an interest part (rent on the current balance) and a principal part (what actually chips away at the loan). Early on, interest is the majority. See it live: $180,000 at 6% over 30 years — the schedule table shows the split for every payment →
Common slips
(1) Used the annual rate instead of monthly. Interest portion = balance × (r/12), not balance × r. (2) Subtracted the full payment from the balance. Only the principal reduction comes off the balance — not the whole $1,400. (3) Confused interest portion with total interest paid. This question is about one month, not the whole loan.
04 Practice — Step by Step
Practice this problem step by step
Mortgage balance $180,000 at 6% APR. Monthly payment $1,300. Split it into interest, principal reduction, and new balance.
Step 1

Compute the interest portion

Interest = balance × (r/12) = 180,000 × (0.06/12). Type just the number.
interest = $
Step 2

Compute the principal reduction

Principal reduction = M − interest = 1,300 − 900.
reduction = $
Step 3

Compute the new balance

New balance = old balance − reduction = 180,000 − 400.
new balance = $
Q4 Q6
MAT-144 · TOPIC 04 · REVIEW · Q5 OF 06