COMPOUND INTEREST - ANSWERS

1.  On the first of January, Tessa puts her generous Christmas present of £500 in the building society which offers an interest rate on savings accounts of 7.2%

How much are her savings worth?:
a) at the end of the 3rd year
b) at the end of the 6th year

You can set this out in a table like the one shown on the questions page or as a shortcut use the formula:

£C(1 + i / 100)n

Where:
C = Initial amount invested (C stands for Capital)
i = The interest rate in %
n = The number of years

Note that it's probably best to use a table in exams, unless you are told to use any method you like - you can still use the formula to check your answers though!

a) £615.96
b) 758.82

Remember, any answers to do with money cannot be more than 2 decimals places.

2.  Nigel and Jane rent a house for a monthly rent of £350. The rent agreement says that the rent will be reviewed annually and increased by the annual inflation rate. If the annual inflation rate is 3%, calculate:

a) The amount of rent paid in the first year
b) The rent increase at the end of the first year
c) The monthly rent paid during the second year

a) 12 months in a year so, 12 x £350 = £4,200

b) 3% of £350 = 0.03 x £350 = £10.50 per month

c) 12 x £360.50 = £4,326

where £360.50 = the monthly rent in the first year £350 plus the increase of £10.50 for this year.

3.  A new car costs £18,000. It depreciates (loses value) at a rate of 10% each year.

How much is the car worth?
a) After 3 years
b) After 6 years

 

Here it is possible to use the formula again though we now need to decrease by the percentage rate so the formula is change slightly:

£C(1 - i / 100)n

a) £13,122

b) £9,566

4. £1,500 is invested for 5 years in an investment account which pays 7.8% interest. How much is the investment worth at the end of the 5th year:

a) if the account pays compound interest
b) if the account pays simple interest

 

a) £2,183.66

b) Interest in 1 year = £1,500 x 0.078 = £117

hence the interest in 5 years is 117 x 5 = £585

So the total value = £1,500 + £585 = £2,085

5. £250 is invested for 3 years in an account which pays 7% per annum compound interest. What single number can you multiply £250 by to get the total amount at the end of the 3rd year?

Total = 306.26

Let x be the number:

250x = 306.36

x = 306.36 / 250 = 1.225

6.  £5,000 is invested for 4 years at 8% compound interest per year. What is the total interest earned over the four years?

Total amount = £6.802.44

Subtract the initial amount to get the total interest:

£6,802.44 - £5,000 = £1,802.44

7. If £3,000 is invested in an account where the interest is paid at 5% every six months. What is the total interest earned after two years?

After 2 years the interest is actually paid 4 times at 5%.

£3,646.52 - £3,000 = 646.52