1. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton 2012 1.9 Compound interest

2. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton 2012 Compound interest If money is borrowed and the interest paid is compounded, this can have a large impact on the amount that needs to be paid back. In the example below, £1000 is borrowed for 4 years at an annual interest rate of 5% compounded yearly. Number of years 01234 Total amount owed (£) 100010501102.501157.631215.51 ×1.05 An interest rate of 5% is equivalent to a multiplier of ×1.05 i.e.

3. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton 2012 Compound interest After 4 years of compounded interest, the multiplier of ×1.05 has been applied four times. i.e. The multiplier is applied to the amount owed each year. represents the total amount owed after 4 years. To calculate the amount of interest paid, subtract the initial loan from the total amount owed. i.e.

4. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton 2012 Compound interest The formula for calculating the amount of compound interest paid on a loan Let I = interest paid C = capital (amount loaned) r = percentage interest rate n = number of time periods