Interest is rent paid for money

Interest is what you pay for the time you keep somebody else's money. Simple means the rent is charged only on the original sum.

The three things it depends on

All three are direct proportions, which is why they simply multiply together.

The formula

\[ I = \frac{P \times R \times T}{100} \]

Symbol	Name	What it means
P	Principal	The sum lent or borrowed at the start
R	Rate	The percentage charged for each year
T	Time	How long, measured in YEARS
I	Interest	The rent paid, which is the extra money
A	Amount	Principal plus interest, the total handed back

Time must be in years

Nine months is 0.75 years. Putting 9 into the formula gives an answer twelve times too large.

Interest and amount are not the same

The interest is the extra money only; the amount is principal plus interest. Read the question to see which is being asked for.

Rearranging to find anything

To find the rate, R = 100I ÷ PT. Rather than memorising four versions, remember one and rearrange.

Simple interest does not grow on itself

At 10 per cent, 1000 rupees earns exactly 100 every single year, including the tenth. The interest already earned never earns anything itself.

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Worked Example 1

Rs 10000 is deposited at 8% per year for 3 years.

List what you knowP = 10000, R = 8, T = 3

Put them into the formulaI = 10000 × 8 × 3 ÷ 100 = Rs 2400

Now find the amountA = 10000 + 2400 = Rs 12400

Check by years800 a year × 3 years = 2400. Each year earns exactly the same.

Worked Example 2

Rs 5000 is borrowed at 12% per year for 9 months.

Convert the time to years firstT = 9 ÷ 12 = 0.75 years

Now use the formulaI = 5000 × 12 × 0.75 ÷ 100 = Rs 450

What the wrong answer looks likeUsing 9 gives Rs 5400, which is twelve times too large.

Sense checkA full year would earn 600, so nine months must earn less. 450 is three quarters of 600.

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Activity 20.1

Build a ten year interest table

What you needSquared paper ruled into four columns, and a pencil. No calculator for the first few rows.

MethodStart with Rs 1000 at 10%. Fill a row for each year from 1 to 10.

Then compareNow do a second table where each year the interest is worked out on the previous amount instead.

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Interest is rent paid for the use of somebody else's money.

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1What is interest, and what makes simple interest simple?

2Why must the time be converted into years before using the formula?

3What is the difference between the interest and the amount?

4How do you find the rate of interest when you know the principal, the amount and the time?

5Why does simple interest fall behind an account that pays interest on interest?

Question 1 of 10

1Simple interest is charged on

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Unit 20 · Simple Interest

Simple Interest

Mathematics · Grade 7

What You Will Be Able To Do

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Work out interest from the principal, the rate and the time

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Convert months into years before anything goes into the formula

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Rearrange the formula to find the rate, time or principal

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Explain why simple interest falls behind an account that grows on itself

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Interest is rent paid for money. The word simple means the rent is charged only on the original sum, never on the interest that has already built up.

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Presenter notes: Open with a question that grounds the whole topic. If you lend a friend your bicycle for a month, is it reasonable to expect something in return? Most will say yes, and that is exactly what interest is: a payment for the use of something, in this case money, for a length of time. Then ask what a bank actually sells, and let the class arrive at the answer that it sells the use of money.