OCR GCSE Mathematics (J560) — Ratio, Proportion and Rates Of Change
When you borrow money from a bank, they do not let you use it for free. The extra money you must pay back is called interest, and it is calculated based on the initial sum of money, known as the principal.
To find the interest and the final balance, you need two key formulas. Note that these are not provided on the OCR formula sheet, so you must memorise them.
First, calculate the total interest earned or charged:
Where:
Next, calculate the total amount (the final balance or total repayment):
Amina invests £1,500 in a savings account offering 4% simple interest per annum. Calculate the total balance in her account after 3 years.
Step 1: State the formula and identify the variables.
Step 2: Substitute the values into the formula to calculate the total interest.
Step 3: Calculate the total amount using the formula Total = Principal + Interest.
Final Answer:
Simple interest appears in several different real-world scenarios in OCR exams:
It is vital that the time units match the interest rate frequency. This is called unit synchronisation. If a bank offers an interest rate per annum, but the money is invested for 6 months, you must convert the time into years before using the formula ( years).
Sometimes, an exam question will give you the starting principal and the final total amount, asking you to find the interest rate or the time period.
Students frequently calculate the total interest () and stop there. Always check if the question asks for the 'interest earned' or the 'total balance' ().
In 'Calculate' questions, examiners expect to see clear substitutions into the simple interest formula; writing will often secure you a method mark even if you make a calculation error.
Always check that your time value matches the interest rate. If the rate is 'per annum' but the duration is 18 months, you must use in your calculation.
Unless an OCR question tells you otherwise, always round financial answers to 2 decimal places (e.g. £87.50, not £87.5).
Simple interest
A method of calculating interest where the interest amount is exclusively based on the original starting amount and remains constant each period.
Principal
The initial sum of money invested, saved, or borrowed before any interest is added.
Interest rate
The percentage of the principal that is charged or earned over a specific time period.
Per annum
A Latin term meaning "each year" or "annually", used to describe how often an interest rate is applied.
Total amount
The final balance of an account or the total repayment of a loan, found by adding the accumulated interest to the principal.
Hire purchase
A financial agreement where a buyer pays an initial deposit and pays off the remaining balance plus simple interest over a set period.
Deposit
An initial upfront payment made at the start of a hire purchase agreement.
Depreciation
The reduction in the value of an asset over time. In the context of simple interest, this refers to losing a fixed percentage of the original value each period.
Put your knowledge into practice — try past paper questions for Mathematics
Simple interest
A method of calculating interest where the interest amount is exclusively based on the original starting amount and remains constant each period.
Principal
The initial sum of money invested, saved, or borrowed before any interest is added.
Interest rate
The percentage of the principal that is charged or earned over a specific time period.
Per annum
A Latin term meaning "each year" or "annually", used to describe how often an interest rate is applied.
Total amount
The final balance of an account or the total repayment of a loan, found by adding the accumulated interest to the principal.
Hire purchase
A financial agreement where a buyer pays an initial deposit and pays off the remaining balance plus simple interest over a set period.
Deposit
An initial upfront payment made at the start of a hire purchase agreement.
Depreciation
The reduction in the value of an asset over time. In the context of simple interest, this refers to losing a fixed percentage of the original value each period.
