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

Forward direction this time: given P, r, and t-in-months, find the interest owed and the total repayment amount.

01 Worked Example Video

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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

Manuel takes a loan for his college tuition at 19% simple annual interest. Loan: $3,200 for 5 months.

What’s the total amount owed after 5 months (assuming no payments)? Type just the number, rounded to the nearest cent.

Do not round intermediate computations.

A = $

Sasha's loan

Sasha takes a loan at 14% simple annual interest. Loan: $2,500 for 8 months.

What’s the total amount owed after 8 months (assuming no payments)? Type just the number, rounded to the nearest cent.

Do not round intermediate computations.

A = $

Dion's loan

Dion takes a loan at 17% simple annual interest. Loan: $4,800 for 6 months.

What’s the total amount owed after 6 months (assuming no payments)? Type just the number.

Do not round intermediate computations.

A = $

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

I = P × r × t same simple-interest formula as Q1

Convert months → years first t = m / 12 (keep it a fraction)

This is Q1 with a twist: the term arrives in months (or days). Convert to years before you plug in, and don’t round the fractional-year value. Then compute I, then A.

Common slips

(1) Used t = 5 instead of 5/12. Off by 12×. (2) Rounded 5/12 to 0.42 early. Costs cents in the final answer. ALEKS says “do not round intermediate computations.” (3) Stopped at I. Part (b) asks for the amount owed = P + I.

04 Practice — Step by Step

Practice this problem step by step

A $2,400 loan for 8 months at 6% simple annual interest. Find the amount owed at the end of the term.

Step 1

Convert time to years

The term is 8 months. What’s t in years?

Step 2

Compute the interest

Compute I = 2,400 × 0.06 × (8/12). Type just the number.

I = $

Step 3

Compute the amount owed

Add the interest to the principal to get the amount owed.

A = $

Q16 Q18

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

You walked the months-term simple loan end to end.