Calculating Interest

Key Facts and Exam Tips

• When saving money, interest is normally paid to the saver.
• When borrowing money, the borrower is normally charged interest by the lender.
• The rate of interest is usually given as a percentage.
• Most examination questions tell you the interest rate per annum. This means ‘per year’.
• The principal is the amount of money (deposited or borrowed) that you started with.
• With simple interest, the amount you invest (the principal) earns a certain amount of interest each year. The principal remains the same.
• With compound interest, the amount you invest (the principal) doesn’t stay the same. Your investment grows more quickly because every year the interest you earn is added on to the principal.
• Examination questions may ask you to find the total interest paid over a period of time.
• In order to calculate the amount of interest, you should know how to find a given percentage of an amount of money.
• The simple interest will be the same each year and you will be told the number of years in the question.
• The compound interest is added on to the principal (usually exam questions state that it is added at the end of each year). When calculating with compound interest you need to work out the new principal at the start of each new year and then find the interest that will be gained over the year. Repeat this process for the number of years given in the question.
• The total compound interest paid can be found by subtracting the original principal from the final principal. It is the difference between the amount originally invested and the total amount after a period of time.
• You should know how to express a percentage as a decimal and recognise that, for example, an increase of 15% can be calculated by multiplying by 1.15.
• Questions on compound interest may ask you to find the total invested (the final principal) at the end of a number of years. If you can use a calculator to do this, it is often easier to multiply repeatedly by 1.15 (if the interest rate is 15%). You can also use the index functions on your calculator to express the number of years that you do this for as a power.
• It is sensible to round amounts of money to the nearest penny at the end of the calculation.
• Questions on depreciation by a percentage amount may also be set. When something depreciates over time this means it loses value. Here you subtract to calculate the new value at the end of a year.