Calculating the amount of a loan

Question

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

Answer 1

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.