APR

Apr 19, 2005 2 Replies
F

I have a query about calculating APR on a loan.



I just got the following quote for £6k over 12 months from ZOPA

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"Based on your credit rating you can borrow from the A market at 7.30%.



Your monthly repayment would be £519.34 Your total repayment would be £6,232.14 (includes 0% Zopa fee of £0.00) The APR for this loan would be 7.30%"



Now, so far as I understand it, the APR reprensents the true annualised cost of the loan including all fees. AFAII, the pattern of cash flows for this loan would be:



Month DR CR



00 6000.00
01 519.34
02 519.35
03 519.34
04 519.35
05 519.34
06 519.35
07 519.34
08 519.35
09 519.34
10 519.35
11 519.34
12 519.35

---------------------- Total 6232.14 6000.00



----------------------



So the loan would cost me £232.14 in interest.



Now, to my simple brain, it looks like you've got value of £3000.00 across the year, because you're paying down the borrowing in a straight line.



Calculating £232.14 / £3000.00 give me 7.74%, not the 7.30% quoted.



Where have I (or, less likely, Zopa) gone wrong ?



Nick



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R

Your first approximation, of the mean balance being half the amount borrowed, is too rough.

Even assuming the (rough) model of linear pay-down, the balance during the whole of the first month will be £6k, and during the whole of the 12th month will be £500. So really the mean balance during the year will be £3250, and 232.14/3250 is 7.14%.

That's not a much better approximation, but at least it errs on the right side.

What you really need to do is back-apply the APR to each payment to see what it would have been worth in month 0. If they then all add up to £6k, all is well.

So, an APR of 7.3% corresponds to a yearly factor of 1.073, or a monthly factor of the 12th root of that: 1.0058888. Divide £519.345 by that, and the first monthly payment is worth £516.30, and the others, complete with running totals, are:

1 516.3046 516.3046 2 513.2820 1029.5865 3 510.2770 1539.8636 4 507.2897 2047.1533 5 504.3199 2551.4731 6 501.3674 3052.8405 7 498.4322 3551.2728 8 495.5142 4046.7870 9 492.6133 4539.4003 10 489.7294 5029.1298 11 486.8624 5515.9921 12 484.0121 6000.0042

Spot on.

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J

In message , snipped-for-privacy@hotmail.com writes

Ronalds answer is right, but if it helps, I've put the base of your error below.

You dont pay the borrowing off in a straight line, you pay more interest at the beginning.

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