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 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.

Diego's food truck loan v1

Diego borrowed money from a bank to open a food truck. He took out a personal, amortized loan for $30,000, at an interest rate of 7%, with monthly payments for a term of 4 years.

(a) Find Diego's monthly payment.
(b) If he pays the monthly payment for the full term, find his total amount to repay the loan.
(c) Find the total amount of interest he will pay.

Aisha's wedding loan v2

Aisha took out a personal, amortized loan for $18,500 to cover wedding expenses, at an interest rate of 8.25%, with monthly payments for a term of 3 years.

(a) Find Aisha's monthly payment.
(b) Find her total amount to repay the loan.
(c) Find the total amount of interest she will pay.

Mateo's bike loan v3

Mateo took out a personal, amortized loan for $8,400 to buy a touring bike, at an interest rate of 6.5%, with monthly payments for a term of 5 years.

(a) Find Mateo's monthly payment.
(b) Find his total amount to repay the loan.
(c) Find the total amount of interest he will pay.

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

M = P(r/12) / (1 − (1 + r/12)^−12t)
total = M × 12t
interest = total − P

Three formulas, one chain. Get M first, then everything else falls out of arithmetic.

Name the four pieces and convert.

P = $30,000. r = 0.07 (7% as a decimal). t = 4 years. So r/12 ≈ 0.005833 and n = 12t = 48 total payments.

Plug into the L2 formula for the monthly payment.

Compute the denominator (1 − 1.005833^(−48)) first, then divide.

M = (30,000 \times 0.005833) / (1 - 1.005833 -48) \approx $718.39

Total to repay, then total interest.

Multiply M by 48 payments. Then subtract the original principal to isolate interest.

total = 718.39 \times 48 \approx $34,482.59 interest = 34,482.59 - 30,000 \approx $4,482.59

Sanity check: ~15% of the loan paid in interest over 4 years on a 7% loan. About right.

▸ COMMON SLIPS(1) Used 7 instead of 0.07. Always convert percent to decimal before plugging in. (2) Forgot to divide r by 12. The formula uses the monthly rate. (3) Confused total cost with total interest. Total cost = M × n; interest = total − principal.

04 Practice — Step by Step

Try a different scenario. Same recipe — monthly first, then total, then interest.

Compute the monthly payment.

Aisha's $18,500 wedding loan at 8.25% APR for 3 years. What's the monthly payment?

M = $

Compute the total amount to repay.

From step 1: monthly = $581.55, term = 3 years. What's the total amount Aisha will repay?

total = $

Compute the total interest.

From step 2: total to repay = $20,935.80; principal = $18,500. How much of that is interest?

interest = $

▸ 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.

Topic overview Q2