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What is the amount of loan that costs £45 when repaid after 1 year when the interest rate is 9% per annum?

So, far I have got 45/0.09=500

but, could it also be 45/1.09 ≈ 41.28

user3184807
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  • The loan "costs" £45 might mean that the cost of loss of opportunity to the lender is that much. I think 500 is more plausible. – tpb261 May 28 '14 at 08:09

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The 500 answer is implausible (you loan 500 and repay 45? Not how the world works...).

If we loan $x$ and pay 9% interest we have to repay $x$ plus $0.09x$ in interest. So we repay $1.09x = 45$ after a year, so indeed $x = \frac{45}{1.09}$ as was your second idea.

Henno Brandsma
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  • I think the word "costs" is very important here. The loan "costs" £45 must mean that the cost of the money is that much, so 500 is more plausible. It doesn't mean that £45 is repaid. It is the price you are paying to the lender for his loss of opportunity – tpb261 May 28 '14 at 08:07
  • @tpb261 I think this is a matter of interpretation, that the OP should disambiguate. – Henno Brandsma May 28 '14 at 09:28
  • Agree with it. But I think now I have left the OP confused again :) – tpb261 May 28 '14 at 09:31