Apr Maths Question

C

Craig_uk

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Jul 28, 2004
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Hopefully one of the Maths guys (or gals) can help me with this one.

How do you work out the APR of a loan.

I know this gets provided but I'd like to know how to do this myself just because I like to check these things.

So for example.

Lets say I'm getting £6000 over 36 months, monthly repayment is £186.73, so total repayment is £6,722.34

What is the calculation used to get the APR ?

Thanks!
 
Do you not just divide the total paid by the total borrowed to get the APR? In this case 12%?
 
No, the APR on the figures I gave you is 7.8%, I'd like to know how to work this out, rather than confuse my little brain i thought someone on here might know.
 
Originally posted by PDJ@May 30 2006, 09:37 PM
Do you not just divide the total paid by the total borrowed to get the APR? In this case 12%?
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It's a good job you don't teach maths, PDJ! :D Firstly, using your calculation the annual interest would be approximately 4%, as the loan is over three years. But as the interest is paid on an ever decreasing balance of capital borrowed you can see why that wouldn't be correct.

Craig, the best thing to do would be to download one of the programs available on the net to do the calculation. The one on the FISA site is only 51 kB:

FISA APR Calculator
 
Originally posted by Craig_uk@May 30 2006, 11:01 PM
But wanted to know how to do this manually.
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OK, you asked for it, and good luck. The formula is:

L - F = P1/(1 + i) + P2/(1 + i)2 +… (Pn + Bn)/(1 + i)n

Where:

i = APR

L = Loan amount

F = Points and all other lender fees

P = Monthly payment

n = Month when the balance is paid in full

Bn = Balance in month n

But this equation can be solved for i only through a series of successive approximations, which must be done by computer. Many calculators will also do it provided that all the values of P are the same.
 
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