You have just purchased a car with a $£20,000$ price tag. The dealer offers to let you pay for your car in $5$ equal annual instalments, with first payment due in a year. If the dealer finances your purchase at an interest rate of $10\%$, your annual payment will be $$ \text{a) } £4,4004$$ $$\text{b) } £6442.04$$ $$\text{c) } £4,000$$ $$\text{d) } £5,275.95$$
I have worked out the answer via trial and error, but does anyone have a more solid way of working this out.
Any help appreciated thanks!
You want
$20000=\dfrac{x}{1.1^1}+ \dfrac{x}{1.1^2}+ \dfrac{x}{1.1^3}+ \dfrac{x}{1.1^4}+ \dfrac{x}{1.1^5}$
so
$x=\dfrac{20000}{1.1^{-1}+1.1^{-2}+1.1^{-3}+1.1^{-4}+1.1^{-5}}$
which is
$20000\times \dfrac{1.1^6-1.1^5}{1.1^5-1}$.