Simple Interest and Percentages in Finance

Simple interest is calculated on the original principal only. The formula I = PRT links the interest, principal, rate, and time. Compound interest is briefly introduced as interest on interest.

Simple Interest

Simple interest is earned (or charged) on the original amount of money (the principal) only.

Simple Interest Formula

I = P \times R \times T

I = interest earned, P = principal (starting amount), R = annual interest rate (as a decimal), T = time in years

Converting a percentage rate to a decimal

If the rate is 5%, write it as $R = 0.05$ (divide by 100).

Bank account — simple interest

You deposit £400 into a savings account at 3% per year for 2 years.

$I = 400 \times 0.03 \times 2 = £24$

Total in account after 2 years: $£400 + £24 = £424$

Finding the Total Amount

$\text{Total} = P + I = P + PRT = P(1 + RT)$

Compound Interest (Introduction)

With compound interest the interest from each year is added to the principal, so you earn interest on your interest.

Note

Compound interest formula: $A = P(1 + r)^t$ , where $r$ is the annual rate as a decimal and $t$ is years. This is studied in more detail in higher years — for now, understand why compound interest grows faster.

Year	Simple (3%, £400)	Compound (3%, £400)
1	£412	£412
2	£424	£424.36
3	£436	£436.91
5	£460	£463.71

Notice compound interest pulls ahead over time.

Real-World Examples

Real world: savings account

You deposit £1,000 in a savings account at 3% per year for 5 years.

$I = 1\,000 \times 0.03 \times 5 = £150$

Total balance: £1,000 + £150 = £1,150. Banks use simple interest for easy-access savings accounts where you can withdraw at any time.

Real world: personal loan

You borrow £500 at 8% per year and repay in full after 2 years.

$I = 500 \times 0.08 \times 2 = £80$

Total repayment: £500 + £80 = £580. Comparing loan offers means checking both the interest rate and the loan term.

Real world: government savings bond

A savings bond offers 4% simple interest per year on a £2,000 investment for 3 years.

$I = 2\,000 \times 0.04 \times 3 = £240$

Total returned: £2,000 + £240 = £2,240. Governments issue bonds to raise capital, paying predictable interest to investors in return.

Practice Problems

Calculate simple interest on £600 at 4% per year for 3 years.

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I = 600 × 0.04 × 3 = £72. Total = £672.

How long will it take £500 to earn £75 simple interest at 5% per year?

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T = I ÷ (P × R) = 75 ÷ (500 × 0.05) = 75 ÷ 25 = 3 years.

At what annual rate must £1000 be invested to earn £200 simple interest in 4 years?

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R = I ÷ (P × T) = 200 ÷ (1000 × 4) = 200 ÷ 4000 = 0.05 = 5% per year.