# PayDay loan APR

I'm not convinced I'm getting the correct figure when I calculate an APR rate.

I have an amount I want to loan £100 I want to pay this back in 14 days. Interest for this loan is 15% The fee for this service is 0.20p per day. From this I calculate the fee to be £17.80

So, my calculation to get APR is as follows

APR = ((117.80-£100/£100)/((14/365)*100))

I get 2970%

Is this correct? Or is my formula wrong?

Any help would be greatly appreciated

Jonah

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Assuming the fee is paid at the end of the loan, I would do $$\left(\frac{100+100\times 0.15+0.2\times 14}{100}\right)^{365.25/14}-1 \approx 70.80$$ so an APR of about 7080%.

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7080%?? The APR would be that high? Surely it would be lower than this. –  Jonah Oct 31 '12 at 22:58
@Jonah: you have 17.8% compounded more than 26 times –  Henry Oct 31 '12 at 23:04
Cheers Henry. Thanks for this. –  Jonah Oct 31 '12 at 23:25
Hi Henry, a while a go you answered this question for me, I've had to come back to it as there is something I don't understand. On this website Payday loan firm the APR, stays relatively low and doesn't go over 773.80% if a customer borrows \$250 over 7 days. How are these guys keeping the APR low. I'm sure I've used the same formula as them. –  Jonah Jan 14 '13 at 14:32
Perhaps they took the confusing "continuously compound rate": taking the natural logarithm of 1333.0473 gives 7.1952 which might improperly be written 719.52% which is closer to the figure you quote. Highly misleading: suppose you rolled over the amount each week and paid a compound weekly interest rate of 14.84%. After 52 weeks you would owe 333261.82 –  Henry Jan 15 '13 at 9:31
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