6. A car was purchased for \(\pounds 18000\) on 1 st January.
On 1st January each following year, the value of the car is \(80 \%\) of its value on 1st January in the previous year.
- Show that the value of the car exactly 3 years after it was purchased is \(\pounds 9216\).
The value of the car falls below \(\pounds 1000\) for the first time \(n\) years after it was purchased.
- Find the value of \(n\).
An insurance company has a scheme to cover the maintenance of the car. The cost is \(\pounds 200\) for the first year, and for every following year the cost increases by \(12 \%\) so that for the 3rd year the cost of the scheme is \(\pounds 250.88\)
- Find the cost of the scheme for the 5th year, giving your answer to the nearest penny.
- Find the total cost of the insurance scheme for the first 15 years.
\section*{LU}