6. At the beginning of the year 2000 a company bought a new machine for \(\pounds 15000\). Each year the value of the machine decreases by \(20 \%\) of its value at the start of the year.
- Show that at the start of the year 2002, the value of the machine was \(\pounds 9600\).
When the value of the machine falls below \(\pounds 500\), the company will replace it.
- Find the year in which the machine will be replaced.
To plan for a replacement machine, the company pays \(\pounds 1000\) at the start of each year into a savings account. The account pays interest at a fixed rate of \(5 \%\) per annum. The first payment was made when the machine was first bought and the last payment will be made at the start of the year in which the machine is replaced.
- Using your answer to part (b), find how much the savings account will be worth immediately after the payment at the start of the year in which the machine is replaced.