Credit cards, loans and mortgages consist of borrowing money from a bank. Banks make money from the loans by charging interest, which is a cost that is then added to the loan. Interest rates are shown as APR (Annual Percentage Rate).

At the end of each month, the interest for the month is added to the current balance. The borrower then pays an agreed sum of money which reduces the amount borrowed, and this new total is the starting amount for the next month.

Sam borrows £4,000 for a car. He is told that the monthly interest rate is 0.8%. He will pay back the loan at £400 per month. How much of the loan will he have paid off after three months?

The interest, each month, is calculated from the loan at the start of the month x `frac(0.8)(100)`.

For month 1, this is 4000 x `frac(0.8)(100)` = £32.00.

At the end of the first month he owed £4000 + £32 - £400 he repaid for a new total of £3632. This is the starting amount for next month.

month | loan | interest | repaid | new amount |

1 | 4000.00 | 32.00 | 400.00 | 3632.00 |

2 | 3632.00 | 29.06 | 400.00 | 3261.06 |

3 | 3261.06 | 26.09 | 400.00 | 2887.15 |

The amount paid off is £4000.00 - £2887.15 = £1112.85.

Answer: £1112.85

Jonny borrows £2,000 for a holiday on a credit card. The interest rate is 1.2% per month. He plans to pay back the loan at £25 per month. Is this enough to start reducing the amount of the loan?

Interest due is £2,000 x `frac(1.2)(100)` = £24.00.

He is paying £25 per month, so this will reduce the loan by £1.

Answer: Yes

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).