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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!

user3184807
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Aj1990
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1 Answers1

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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

$20000\times \dfrac{1.1^6-1.1^5}{1.1^5-1}$.

Henry
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