### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Simple Interest

Interest is either earned when we deposit money into a bank or paid when we borrow money. Simple interest is calculated using a straightforward formula that considers the principal amount, the interest rate, and the time for which the money is deposited or borrowed.

## Formula for Simple Interest

The formula for simple interest is: Where:

• Simple interest earned or paid
• Principal amount (money deposited or borrowed)
• Rate of interest (as a percentage, e.g., 5%, 12%, etc.)
• Time (in years)

Let’s look at some examples.

## Examples

Example 1: Calculating the Final Amount after Interest

Mr White deposited £5000 into a bank for 5 years, earning 2% interest on his money per year. How much will he have in his account after the 5 years? Principal amount  Rate of interest  Time years

Interest: The interest for 5 years is £500. So, at the end of 5 years, Mr White will have £5000 (principal) + £500 (interest) = £5500 (final amount).

Example 2: Calculating Interest and Total Amount Paid for a Loan

Bernard took a loan of £10,000 from his bank and will pay interest on this sum for 10 years at the rate of 5% per annum. Find how much interest he should pay after 10 years and the total amount he paid.  % years

Using This is the interest Bernard will pay after 10 years. The total amount of money to be repaid is £10,000 (principal) + £5,000 (interest) = £15,000 (total amount paid).

Example 3: Finding the Amount Borrowed

A sum of money was borrowed from a bank at a 7.5% interest per year for 4 years. The interest amounted to £150. What is the amount borrowed?

Using and is unknown:    The amount borrowed is £500.

Example 4: Finding the Interest Rate per Annum

£50,000 was paid to Mrs Mary after investing £40,000 for 6 years into a bank. Find the interest rate per annum.

Using with and years, we have:     % (to one decimal place)

Example 5: Finding the Loan Duration

A sum of £4500 was borrowed from a firm paying 2.5% interest rate per annum. The interest paid was £750. Find how long the sum was loaned.

Using with , , and , we have:    years years, months

Example 6: Calculating Interest Earned in a Specific Time Period

£500 is deposited into a bank paying a 3% interest rate per annum. How much interest is earned in 4 months?

Using with , , and (4 months is of a year), gives:  The interest earned in 4 months is £5.