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 Worked Example Video

Every step of Finding the principal, rate, or time for a simple interest loan whose term is given in months or days explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

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

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? Type just the number.

Do not round intermediate computations.

P = $

James

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? Type just the number.

Do not round intermediate computations.

P = $

Sara

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? Type just the number.

Do not round intermediate computations.

P = $

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

Start with I = P × r × t solve for the missing piece

Solving for P P = I / (r × t)

Same simple-interest formula as Q1, just rearranged. The trap: the term is in months, but the rate is annual. Convert months to years (m/12) before plugging in — and don’t round the fraction.

Common slips

(1) Used t = 5 (months) instead of 5/12 (years). Off by a factor of 12. (2) Rounded 5/12 to 0.42. ALEKS explicitly says “do not round intermediate computations” — keep the fraction or carry many decimals (0.41666…). (3) Used r = 4.8 instead of 0.048. Rate must always be a decimal.

04 Practice — Step by Step

Practice this problem step by step

A 6-month loan at 5% simple annual interest charged $75 in interest. How much was borrowed?

Step 1

Convert time to years

The term is 6 months. What’s t in years?

Step 2

Compute r × t

Multiply 0.05 × 0.5 (the denominator of the P formula).

r × t =

Step 3

Solve for P

Compute P = I / (r × t) = 75 / 0.025. Type just the number.

P = $

Q13 Q15

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

You walked the reverse simple-interest move end to end.