Simple Interest

15 min

Let's begin

Keza saves 20 000 Frw in her family's Umurenge SACCO account. One year later she checks her balance and finds 21 000 Frw. She did not put in any more money. Where did the extra 1 000 Frw come from?

The SACCO paid her interest: a reward for letting it keep and use her money. In this lesson you will learn to calculate interest yourself.

The words you need

Principal (P): the money saved, lent or borrowed at the start.
Rate (R): the percentage paid each year, for example 5% per year.
Time (T): how long the money is kept, in years.
Interest (I): the extra money. A saver earns interest from the SACCO or bank. A borrower pays interest to the lender.

Simple interest

With simple interest, the interest is worked out on the original principal only, so you get the same amount of interest every year. The formula is:

I = P × R × T ÷ 100

We divide by 100 because the rate is a percentage. (Some books write I = Prt with the rate as a decimal, such as 5% = 0.05. It is the same calculation.)

Worked example 1

Keza: P = 20 000 Frw, R = 5%, T = 1 year.
I = 20 000 × 5 × 1 ÷ 100 = 100 000 ÷ 100 = 1 000 Frw. That is the extra 1 000 Frw.

Worked example 2

Mugisha saves 50 000 Frw at 8% per year for 3 years.
I = 50 000 × 8 × 3 ÷ 100 = 1 200 000 ÷ 100 = 12 000 Frw.
Check year by year: each year he earns 8% of 50 000 = 4 000 Frw, and 3 × 4 000 = 12 000 Frw.

Worked example 3

(a loan). Habimana borrows 120 000 Frw at 15% per year for 2 years to start a small shop.
I = 120 000 × 15 × 2 ÷ 100 = 36 000 Frw. This is what the loan costs him.

When the time is in months

The rate is per year, so change months into years: T = number of months ÷ 12. For example, 6 months = 612 = 12 year.

Worked example 4

Find the simple interest on 40 000 Frw at 9% per year for 8 months.
T = 812 = 23 year.
I = 40 000 × 9 × 23 ÷ 100. Step by step: 40 000 × 9 = 360 000, then × 2 ÷ 3 = 240 000, then ÷ 100 = 2 400 Frw.

Tip

Say it like a chant: "P times R times T, over one hundred!" And make sure T is in years before you start.

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Try it yourself

P = 10 000 Frw, R = 6% per year, T = 1 year. Find I.
P = 30 000 Frw, R = 4% per year, T = 3 years. Find I.
Find the interest on 60 000 Frw at 10% per year for 6 months.
Find the interest on 25 000 Frw at 12% per year for 2 years.
Gatete borrows 80 000 Frw at 15% per year for 1 year. How much interest must he pay?

Answers

10 000 × 6 × 1 ÷ 100 = 600 Frw.
30 000 × 4 × 3 ÷ 100 = 3 600 Frw.
T = 12 year. 60 000 × 10 × 12 ÷ 100 = 3 000 Frw.
25 000 × 12 × 2 ÷ 100 = 6 000 Frw.
80 000 × 15 × 1 ÷ 100 = 12 000 Frw.

Quick check

Ineza saves 40 000 Frw at 5% simple interest per year for 2 years. How much interest does she earn?

What you learned today

Principal, rate and time decide the interest.
Simple interest: I = P × R × T ÷ 100, the same amount every year.
Change months into years by dividing by 12.

Sources and credits

6.5 Solve Simple Interest Applications, from Prealgebra 2e by OpenStax, provided by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Mathematics Grade 8, 1.7 Working with money: Budgets, savings, discount, interest and exchange rates, by Siyavula and volunteers, provided by Siyavula, licensed under CC BY 3.0. Adapted by Ganzaa.

1The words you need

2Simple interest

3When the time is in months

Try it yourself

The words you need

Simple interest

When the time is in months