Leaflet through the letterbox - 739.9% APR

"B J Foster" wrote

Would you like to try that one again? It is wrong on soooooo many counts...

"Andrew MacPherson" wrote

That's not just rough, it's waaaaay out! More like 33,650% !!

Far from being way out, it's pretty close: 25% for 14 days becomes 651.8% for 365 days.

"Alec McKenzie" wrote

Rubbish! ...

Imagine borrowing the 125 again at the end of the two weeks. He'd have to pay back

156.25 a fortnight after that, wouldn't he? And if he borrowed that 156.25 for another fornight, then at the end of the six weeks he'd need to pay back 195.31.

That's nearly doubling in six weeks. So it'll be nearly four times as much after just 12 weeks. Wait for 18 weeks (in total), and it'll cost over 745 to pay back -- that's already 645% in only just over 4 months.

Care to guess what he'd need to pay back, if he continued re-borrowing the amount owed each forntight, for a whole year? Yep - he'd have to pay back over 33,000!!

[That's why the APR is over 33,000%.]

Don't you mean 33649%?

You're assuming payments start immediately. If the first payment is due about 16 days after the loan was made, then the APR looks correct.

APR of 739.9% is a weekly rate of 4.1657% (assuming not a leap year).

For 15 weeks at 15 at that rate the loan value at the start of repayments would have to be:

15 * (1-1.041657^-15)/0.041657 = 164.86

So if w is the number of weeks before repayments start, then 1.041657^w 164.86/150

w= log(1.099067) / log(1.041657)

so w = 2.3145, or a bit over 16 days.

"Ronald Raygun" wrote

I deliberately used an approximation, because it changes so much with the exact number of days you use each year.

Yes, it is 33649% using 365.2425 days per year (a good average).

Using 365.25 days, it is 33,653%. For a 365-day year, it is 33,519%. For a 366-day year, it is 34,059%.

But mainly, I just added the nice round figure of

33,000% to Andrew's, ahem, "estimate" of 650%!

Your error lies in treating it as if it were a loan for one year at a compound interest rate (compounded every two weeks), which it is not.

It is simple interest on a loan for two weeks, at an annual rate of 651.8%, and Andrew MacPherson was absolutely correct in what he said.

But that's how APR's are calculated. The APR on such a loan *is* over 33,000%.

"Andy Pandy" wrote

Good idea, but it would have to be more like 23.3 days after...

"Andy Pandy" wrote

"Andy Pandy" wrote

This is where you went wrong - that is the value

**one week before** the first repayment.

The value *immediately* before the first payment would be more like 171.73...

... giving w = 3.3 weeks, or 23.2 days.

Yes, I forgot the repayment formula assumes the first payment is due at the end of the first period...

That may well be how APR's are calculated, which just goes to show that trying to calculate APR for a two-week loan can so easily give you ridiculous results.

The calculations by Andrew MacPherson that triggered this particular thread were not about APR at all, and they were quite correct in their conclusions - that the interest rate was roughly 650%.

"Alec McKenzie" wrote

You can't worm your way out of it that easily!

Andrew's (one and only) comment within this thread was in direct reply to the phrase: "APR 739.9%".

That was the *only* part of the OP's post that Andrew re-posted, and so it should be clear that this is what he was talking about.

52.17

The "650%" figure makes no sense. What use is it? What's the point of quoting it as an annual simple rate?

The APR makes more sense, because that's what you'd pay if you rolled over your loan on the same basis every fortnight for a year. The loan is 25% for a fortnight, equal to an APR of about 33,500%. The "650% per year" figure is meaningless.

With reasonsable interest rates, it may be sensible to quote the annual rate as the periodic rate multiplied by the number of periods. It makes no sense here.

"Andy Pandy" wrote

I very nearly said that myself!

"Andy Pandy" wrote

Totally agree.

"B J Foster" wrote

Eh?

(1) Why use 52.17 when the there are 52.14 weeks in any 365-day year, 52.29 weeks in any

366-day year, 52.18 weeks per year on average in any group of 4 years, or in any group of 400 years ? [Using the modern calendar.]

(2) Does "(1.055565^52.17-1)/100" *really* equal 1533%?

(3) Why are you dividing by 100 anyway??

...

My god, this post has turned into a mathematical debate of epic proportions, I lost count a loooooooooooooooooooooooong time ago :)

Badass.

Okay, since we're going to indulge in hair-splitting: (1) 365.25/7 = 52.17857143 (2) (1.055565^(52.17)-1) = 1579.62% (3) This is an error