Review · Q5 · Computing the interest and repayment amount for a simple interest loan whose term is given in months or days

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.

Manuel's tuition loan v1

Manuel takes out a loan for his college tuition from a bank that charges simple interest at an annual rate of 19%. His loan is for $3,200 for 5 months. Assume each month is 1/12 of a year.

(a) Find the interest that will be owed after 5 months.
(b) Assuming Manuel doesn't make any payments, find the amount owed after 5 months.

Do not round any intermediate computations.

Sasha's loan v2

Sasha takes out a loan from a bank that charges simple interest at an annual rate of 14%. Her loan is for $2,500 for 8 months. Assume each month is 1/12 of a year.

(a) Find the interest that will be owed after 8 months.
(b) Assuming Sasha doesn't make any payments, find the amount owed after 8 months.

Do not round any intermediate computations.

Dion's loan v3

Dion takes out a loan from a bank that charges simple interest at an annual rate of 17%. His loan is for $4,800 for 6 months. Assume each month is 1/12 of a year.

(a) Find the interest that will be owed after 6 months.
(b) Assuming Dion doesn't make any payments, find the amount owed after 6 months.

Do not round any intermediate computations.

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

I = P × r × t
A = P + I

Same simple-interest formula as Q1. The only twist: convert 5 months to 5/12 years before plugging in.

1

Convert time to years.

5 months × (1 year / 12 months) = 5/12 years. Keep this as a fraction or use 0.41666666… — don't round to 0.42.

2

Compute the interest (part a).

Multiply across.

I = 3,200 \times 0.19 \times (5/12) = 608 \times (5/12) = 3,040 / 12 = $253.33

The exact value is $253.3333…; ALEKS asks for the final answer rounded to the nearest cent → $253.33.

3

Compute the amount owed (part b).

Add the interest to the principal. Use the un-rounded I for the addition, round only at the end.

A = P + I = 3,200 + 253.3333... = $3,453.33

▸ COMMON SLIPS(1) Used t = 5 instead of 5/12. Got $3,040 instead of $253.33 — that's a 5-year answer, not 5 months. (2) Used 19 instead of 0.19. Got $25,333 instead of $253.33. (3) Stopped at I. If you wrote $253.33 for part (b), you forgot to add the principal back. A is principal + interest, always.

04 Practice — Step by Step

Same shape with different numbers. Convert months to years first.

1

Interest on a months-long loan.

A 7-month loan of $1,800 at 9% simple annual interest. How much interest accrues?

I = $

2

Reverse: solve for the rate.

An $8,000 simple-interest loan for 6 months charged $200 in interest. What was the annual rate? Type just the number (e.g. 4 for 4%).

r =

▸ 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.