Compound measures

1. Example Find the compound interest on £500 invested for 2 years at 5% per annum. Compound measures 1st Year Amount = 105% of 500 = 1.05 x 500 = £525 2nd Year Amount = 105% of 525 = 1.05 x 525 = £551.25  Compound interest would be £51.25 Alternative method (and preferred) Amount in account after 2 years = 1.052 x 500 =£551.25

2. Example Find the compound interest on £700 invested for 5 years at 3% per annum. 5 Years Amount = (103%)5 of 700 = 1.03 5 x 700 = £811.49 In general If An amount A is invested at p% over n years then Amount after n years =

3. Example A house is bought for £40 000 and appreciates at 9% each year. What will it be worth in 4 years time?

4. Example A motorcycle bought for £1500 depreciates in value by 10% each year. Find the value after 3 years.

5. Example A postage stamp increases in value by 15% each year. If it is bought for £150, what will it be worth in 7 years time?

6. Example In 2013 the population of Burnley was approximately 88 300. However with a reduction of births in the area and other factors the population is said to have decreased at a rate of 3% per year. Based on these figures what is the population likely to be in the year 2020?

7. Example In 1980, Japan was the world’s seventh most populous nation, the population being 114 million and increasing at 1.2% per annum, one of the lowest rates in the world. If the same growth rate continues, what will be its population in 2010?

8. ‘O’ Level paper question The sum of £250 is invested at 5½% per annum simple interest. Calculate the number of years of investment for the total sum to amount to £305.

9. AQA past paper question Nick invests £10 000 for 3 years at 4% per year compound interest. How much interest does he earn?