1
$\begingroup$

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

1 Answers 1

1

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%.

  • 0
    7080%?? The APR would be that high? Surely it would be lower than this.2012-10-31
  • 0
    @Jonah: you have 17.8% **compounded** more than 26 times2012-10-31
  • 0
    Cheers Henry. Thanks for this.2012-10-31
  • 0
    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](http://www.lendup.com) 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.2013-01-14
  • 0
    I cannot repeat their APR calculation. If you borrow 250 and repay 287.10 seven days later then the ratio is 1.1484. Put this to the power of 52 and you get about 1333.0473, i.e. an APR of about 133205%. Higher if you note there are more than 52 weeks in a year.2013-01-15
  • 1
    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 333261.822013-01-15