Finding the principal, rate, or time for a simple interest loan whose term is given in months or days

Reverse direction: given the interest paid, the rate, and the time, solve for the principal. The catch — the term is in months, not years.

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.

Latoya v1

Latoya took out a loan for 5 months and was charged simple interest at an annual rate of 4.8%. The total interest she paid on the loan was $170.

How much money did Latoya borrow? Do not round any intermediate computations.

James v2

James took out a loan for 7 months and was charged simple interest at an annual rate of 5.2%. The total interest he paid on the loan was $182.

How much money did James borrow? Do not round any intermediate computations.

Sara v3

Sara took out a loan for 9 months and was charged simple interest at an annual rate of 6%. The total interest she paid on the loan was $135.

How much money did Sara borrow? 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 → P = I / (r × t)

Same formula, just solved for the missing piece. Convert months to years before plugging in.

Name the pieces. Convert time to years.

I = $170, r = 0.048 (4.8% as a decimal), t = 5/12 years (5 months out of 12 in a year). Solve for P.

ALEKS says "do not round intermediate computations" — keep 5/12 as a fraction or use 0.41666… instead of rounding to 0.42.

Compute the rt product.

Multiply the rate by the time first — both pieces of the denominator.

r \times t = 0.048 \times (5/12) = 0.048 \times 0.4166666... = 0.02

Notice 0.048 ÷ 12 = 0.004 (monthly rate), then × 5 = 0.02. Same answer either order.

Solve for P.

Divide the interest by the rt product.

P = 170 / 0.02 = $8,500.00

Sanity check: 4.8% per year on $8,500 would be $408 in a full year. Over 5 months, that's about $408 × 5/12 = $170. Matches.

▸ COMMON SLIPS(1) Used t = 5 instead of 5/12. Got $708.33 instead of $8,500. The formula needs years, not months. (2) Rounded 5/12 to 0.42. Got $8,432.54 instead of $8,500. ALEKS explicitly says "do not round intermediate computations" — keep the fraction or carry many decimals.

04 Practice — Step by Step

Try a similar reverse problem with different numbers.

Solve for the principal.

A 9-month loan at 6% simple annual interest charged $135 in interest. How much was borrowed?

P = $

Reverse: solve for time (in months).

A loan of $2,000 at 4% simple annual interest accrued $60 in interest. How long was the loan, in months?

t =

▸ 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.

Q1 Q3