Viewing Online On Ground Online sections — 7 topics, discussion questions, one cumulative final In-person sections — 3 units, Exams 1–3, then the final
Course format
MAT-144 · In-person sections Exam 2 Review · Unit 2
Exam 2 Review · Q14

Comparing monthly payments and total costs of two loans

Same formula run twice, then a subtraction. A few tenths of a percent turns into four figures by the end of the term.

01 Worked Example 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.

The cheaper payment

A $45,000 loan over 5 years. Lender A charges 8.9%, lender B charges 8.2%.

What is lender B's monthly payment? Type just the number.

$
The total saved

Same loans: A pays $931.94 a month, B pays $916.75, both for 60 months.

How much less does B pay in total? Type just the number.

$
Long term, tiny gap

A $120,000 loan over 10 years. Lender A charges 7.25%, lender B charges 6.99%.

How much less does B cost in total? Type just the number.

$
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
PMT = P × i ÷ [1 − (1 + i)−N] once per offer
total = PMT × N, then subtract the two totals part (c) wants the TOTAL gap, not the monthly one
When the amount and the term match, the lower rate always wins — there is no arithmetic needed to know which. All the work is in finding by how much, and that answer lives in the totals, not the payments.
Common slips
(1) Reporting the monthly difference. The question asks for the total amount to pay off. (2) Mixing up the two periodic rates. They differ in the fourth decimal place. Label them before you start. (3) Rounding a payment to the dollar before multiplying by N, which shifts the gap by tens of dollars.
04 Practice — Step by Step
Twice through, then compare

Alicia is taking out an amortized loan for $62,000 to expand her bakery and is deciding between two lenders.

(a) An online lender offers a 7-year loan at 10.9% annual interest. Find the monthly payment.
(b) A credit union offers a 7-year loan at 10.5%. Find the monthly payment.
(c) Over the full term, which lender costs less in total, and by how much?

Do not round intermediate computations. Round answers to the nearest cent.

Step 1

How many payments?

Seven years, monthly. Same for both offers.
Step 2

(a) Online lender, 10.9%

i = 0.109 ÷ 12 = 0.0090833333. Find the monthly payment.
$
Step 3

(b) Credit union, 10.5%

i = 0.105 ÷ 12 = 0.00875. Find the monthly payment.
$
Step 4

(c) What does part (c) actually ask?

“Which lender's loan would have the lowest total amount to pay off, and by how much?”
Step 5

(c) By how much?

Online: 1,058.33 × 84 = $88,899.72. Credit union: 1,045.36 × 84 = $87,810.24. The difference?
$
▸ Related Mini Lessons
Q13 Exam 2 Review
MAT-144 · EXAM 2 REVIEW · Q14 OF 14