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I am trying to get better grasp of what the APR figure means, so this example is purely hypothetical.

I have entered a loan of £100,000 into an APR calculator on MoneySuperMarket with a 20% APR for the term of exactly one year. I think quite logically I would expect that the annual rate of 20% to mean around £20,000 paid in interest and fees throughout the year. However, it turns out that the actual cost is only a little more than half of this amount, at £10,228.

Why is the APR not a good prediction of the total cost in this example? Am I being naive in my understanding of what APR is supposed to represent?

The MoneySuperMarket is a UK website, so I expect it its APR calculation adheres to the requirements set by the British Financial Conduct Authority.

Your mistake is that in your calculation of interest ("10%") you divided the total amount of interest paid by the original amount you borrow. However, you don't pay interest for the original amount borrowed, but for the amount you are still borrowing during the time interval for which the interest is due (e.g. every month).

And since the system assumes constant monthly payments, your amount of principal still owed is constantly going down. E.g. after half a year you will have returned almost half of it, and the amount of interest adjusts accordingly.

The APR is the amount of interest that you would pay if you held their money for a whole year. If you borrowed the £100,000 for a year, didn’t pay anything until the end of the year, and then paid it all off, then you would indeed be paying 20%, or £20,000 interest. However, since you are making payments, each month that goes by the interest charges decrease as you pay more of the loan off.

In the first month when you make your payment of £9,185.68, you are charged interest on the entire amount of your loan. The charge is 1/12 of the annual rate, or 1.67%, which would be £1,666.67. This means that £7,519.01 of your loan balance will be paid off with your first payment.

The next month, interest will only be charged on your remaining loan balance of £92,480.98. The interest charges the second month will be £1,541.34, and more of your payment will be going to pay off the loan balance than it did in the previous month.

By the time you get to your last payment, the interest charge will be quite small compared to the first month, as the loan balance will be almost paid off.