Old Style Loan Sharks...

[sandyRoe]

Inspired by posts on Payday Loans. If you borrowed a tenner and repaid the loan with 10 weekly payments of £1.30 what interest were you being charged?

[hc4361]

That isn't 30% APR though.

[Prudie]

No it isn't but to the simple question if I borrow £10 and pay back £13 then I've paid 30% interest. Presumably then Sandy is asking for a wider discussion on APR variations.

[Jonathan-Joe]

To answer Sandy's original question:
You cannot just take the "premium" paid for a loan and call that the interest. I calculate the weekly interest rate to be 4.96% (to 3 significant figures). This translates to 1,139% annual interest rate. This is a mathematical answer, ignoring legal definitions.
This is high, compared to say a 25 year mortgage secured on a property, but I can see why people are happy to use money lenders for low value, short term, no-fuss loans.

So you can check my result:
The amount outstanding at the end of each week:
W1) (10 x 1.0496) - 1.30 = £ 9.20
W2) (9.20 x 1.0496) - 1.30 = £ 8.35
W3) (8.35 x 1.0496) - 1.30 = £ 7.47
W4) (7.47 x 1.0496) - 1.30 = £ 6.53
W5) (6.53 x 1.0496) - 1.30 = £ 5.56
W6) (5.56 x 1.0496) - 1.30 = £ 4.54
W7) (4.54 x 1.0496) - 1.30 = £ 3.46
W8) (3.46 x 1.0496) - 1.30 = £ 2.33
W9) (2.33 x 1.0496) - 1.30 = £ 1.15
W10) (1.15 x 1.0496) - 1.30 = 10 pence overpaid

Taking 52 weeks in a year, this equates to an annual interest rate of ((1.0496 ^ 52) - 1)x100 = 1,139%

[joggerjayne]

Is that right?

Ignoring the marginal weekly variation, in round terms ...

Borrow £10.00

Pay back a total of £13.00 over ten weeks

That's 30% over ten weeks

Multiply that by 5.2 to give the rate over 52 weeks

30 x 5.2 = 156

So the annual rate of interest is equivalent to 156%

No?

[emmie]

not sure if you could work it out from this, but one guy was on a programme last night, might have been late news, about how he borrowed a small amount of money, and got into difficulties repaying it, now it's a large amount of money

https://www.wonga.com/

[Hopkirk]

Wonga now sponsor Newcastle United.

Alan Pardew says he expects his players to give 4010% to every game.

[joggerjayne]

Possibly paying compound interest, em?

(Interest on the interest)

[Jonathan-Joe]

Loan calculations must take account of the following points:-
1) A percentage figure on its own is meaningless, we need the percentage rate, which implies a time element, eg 5% per week, 7% annually.
2) Interest is compounded ie interest is paid on unpaid interest.
3) The amount owed is steadily reduced throughout the term of the loans as each of the regular repayments pays both interest due and part of the loan outstanding.

[Jonathan-Joe]

Nice of the OPer to thank us for our answers.

[sandyRoe]

I've been sitting all night trying to puzzle out if the £3 interest on £10 over 13 weeks was actually a bargain rather than the bit of usury that I think it was.
I've always been of the opinion that a good deed in this naughty world is its own reward. But for those who feel they need an acknowledgement, 'Thank you'.

[Jonathan-Joe]

Sandy, Maybe you're right that those who give a quick, off the top of the head reply shouldn't expect a specific thankyou. But when someone has taken time and trouble to prepare an answer, shouldn't they have confirmation that it has at least been seen? With no response from you, how do I know that the time spent on the calculation that you requested was not wasted?