MAT-144 · Mathematical Reasoning Topic 04 · Loans
Topic 04 · Review · Q1

Finding the monthly payment, total payment, and interest for a loan

Three-part: apply the L2 amortization formula for the monthly, multiply by total months for the lifetime payment, then subtract the principal for total interest.

01 Worked Example Video

Every step of Finding the monthly payment, total payment, and interest for a loan 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.

Diego's food truck loan

Diego borrowed money to open a food truck. He took out an amortized loan for $30,000 at 7% APR, monthly payments for 4 years.

Find Diego’s monthly payment. Type just the number, rounded to the nearest cent.

M = $
Aisha's wedding loan

Aisha took an amortized loan for $18,500 at 8.25% APR, monthly payments for 3 years.

Find Aisha’s monthly payment. Type just the number, rounded to the nearest cent.

M = $
Mateo's bike loan

Mateo took an amortized loan for $8,400 at 6.5% APR, monthly payments for 5 years.

Find Mateo’s monthly payment. Type just the number, rounded to the nearest cent.

M = $
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
M = P(r/12) / (1 − (1 + r/12)−12t) the amortization formula
total = M × 12t interest = total − P
Three formulas, one chain. Get M first, then everything else falls out of arithmetic: total is just monthly × number of payments; interest is total minus the original loan. See it live: $12,000 at 8% over 3 years in the Amortization Sandbox →
Common slips
(1) Used r = 7 instead of 0.07. Always convert to a decimal first. (2) Forgot to divide r by 12. The formula uses the monthly rate r/12, not the annual rate. (3) Confused total cost with total interest. Total cost = M × 12t; interest = total − P.
04 Practice — Step by Step
Practice this problem step by step
A $12,000 amortized loan at 8% APR for 3 years. Walk it through: monthly, total, interest.
Step 1

Compute the monthly payment

With P = 12,000, r/12 = 0.006667, n = 36, compute M. Round to the nearest cent.
M = $
Step 2

Compute total amount repaid

From step 1: monthly = $376.04, term = 36 months. What’s the total repaid?
total = $
Step 3

Compute total interest

From step 2: total = $13,537.44; principal = $12,000. How much of that is interest?
interest = $
Topic overview Q2
MAT-144 · TOPIC 04 · REVIEW · Q1 OF 06