COMPOUND INTEREST

TIP: When doing these sort of problems, remember:

a) Compound interest will be of "interest" to you if you have a building society account, it will tell you how much you savings will be worth next year or in 5 year's time etc. The table below shows how an initial investment of £1,000 can grow in 5 years, if the interest rate is 6%:

Year Amount at start of year Interest Amount at end of year Total Amount at end of year
1 £1,000 1,000 x 0.06 1,000 + 60 £1,060
2 £1,060 1,060 x 0.06 1,060 + 63.60 £1,123.60
3 £1,123.60 1,123.60 x 0.06 1,123.60 + 67.42 £1,191.02
4 £1,191.02 1,191.02 x 0.06 1,191.02 + 71.46 £1,262.48
5 £1,262.48 1,262.48 x 0.06 1,262.48 + 75.75 £1,338.23

Compound interest gives you £338.23 for doing nothing!

b) Simple interest gives you a slightly worse deal:

£1,000 invested for 5 years with 6% simple interest will just give you 6% of £1,000 every year (i.e. £60) multiply this by 5 and we get £300.

 

Solve the following:

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

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

 
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

 

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

 

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?

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

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?

Ok Here's the Answers