James wins the lottery and gets £200,000. He decides to spend 10% of his winnings and invest the rest. From the money he has invested, he receives interest of 3% per year. How much money does James have after 5 years (to the nearest pound)?
James starts with £200,000.
He then spends 10% of his winnings:
200,000*(1-0.1)=180,000
The 1 represents 100%, which the amount of money James starts with. He then spends 10%, which is represented by the -0.1. Therefore 1-0.1 is the remaining 90%
He invests the remaining amount (£180,000) and receives interest of 3% per year for 5 years.
180,000*(1.03)(1.03)(1.03)(1.03)(1.03)=180,000*(1.03)5=208,669.333374~=£208,669
As before, the 1 is 100% before any money has been invested. The 0.03 is the annual 3% interest payment. From above we can rewrite these yearly payments in a quicker format by writing (1.03)5. The final answer is then rounded down to £208,669.
