Interest and Percentages

What you will learn

• Calculate simple interest.
• Find the total, the rate, the time or the principal.
• Compare two offers.

Before you start: you should be able to find a percentage of an amount. See Tax on a Price.

The idea

When you put money in a savings account, the bank uses it, and pays you a fee for the privilege. When you borrow, you pay the lender a fee. That fee is interest, and it is almost always expressed as a percentage of the amount per year.

Key vocabulary

• Principal ($P$): the original amount saved or borrowed.
• Interest rate ($r$): the percentage charged or paid per year, such as $5\%$ per annum.
• Term ($t$): how long the money is saved or borrowed for, in years.

Simple interest

With simple interest, interest is calculated only on the original principal. Each year you earn exactly the same amount:

$I = P \times r \times t$

Simple interest is used for some short-term loans, certain bonds and many classroom problems. Most savings accounts and loans actually use compound interest, where interest is added to the balance and then earns interest itself, but simple interest is the place to start.

Worked examples

Example 1: Interest earned

You deposit £2,000 at $3.5\%$ simple interest per year for $4$ years. How much interest do you earn, and what is the final balance?

1. Convert the rate: $3.5\% = 0.035$.
2. $I = 2000 \times 0.035 \times 4 = 280$.
3. Final balance: $2000 + 280 = 2280$.

Answer: £280 interest; balance £2,280.

Example 2: Months, not years

A £600 loan is charged $12\%$ simple interest per year. How much interest is due after $9$ months?

1. Convert months to years: $t = \frac{9}{12} = 0.75$.
2. $I = 600 \times 0.12 \times 0.75 = 54$.

Answer: £54

Example 3: Finding the rate

An investment of £5,000 earned £450 simple interest over $3$ years. What was the annual rate?

1. Rearrange $I = Prt$ to get $r = \dfrac{I}{Pt}$.
2. $r = \dfrac{450}{5000 \times 3} = \dfrac{450}{15\,000} = 0.03$.
3. Convert to a percentage: $0.03 \times 100 = 3\%$.

Answer: $3\%$ per year.

Example 4: Comparing two offers

Shop A sells a £900 laptop on credit with $8\%$ simple interest over $2$ years. Shop B charges a flat fee of £150. Which is cheaper?

1. Shop A interest: $900 \times 0.08 \times 2 = 144$.
2. Shop B costs £150.

Answer: Shop A is cheaper by £6. Always convert offers into the same form before comparing.

Rates are per year unless stated otherwise. A “1.5% per month” credit card charge is far more than “1.5% per year”, roughly $18\%$ a year even before compounding.

Why it matters

Interest determines how fast savings grow and how much debt really costs. Understanding it helps you compare savings accounts, recognise expensive credit (store cards, payday loans) and judge whether “buy now, pay later” really is a bargain. Financial products in many countries must quote an annual equivalent rate (such as APR or AER) precisely so that people can compare them on equal terms.

This lesson is educational and is not financial advice.