Any Mathematicians or Actuaries here ?

NickX

Hi There,

Following on from another thread where I made a complete hash of working out an APR on a loan, I have been attempting to work out the formula to calculate the APR.

Basically the poster borrows £10,000 and pays back £280 over 60 months, meaning they pay back £16800 over 5 years.

The question is what is the APR ?

Now, I am usually quite good with figures, but this calculation is getting very complicated, so either I am having a mental block or there is a trick that I am missing.

Would be very interested if anyone could advise how to accurately complete this calculation.

Thanks in advance.

PasturesNew

That is 25.1%

You can calculate APR using an online calculator such as this:

http://www.prudentminds.com/loan_calc.html

Just keep guessing/changing the interest rate until the payments match.

sleepless_saver

It's a lot easier to use a calculator than it is to work it out from the basics. But if you really really want to do it, and have a few days to spare for the iterative processes involved, then the government does tell you how it's done (see Part II of this leaflet) .

fermi

If you want the full details of how the OFT state that APR should be calculated, then there is this:

http://www.oft.gov.uk/advice_and_resources/resource_base/legal/cca/apr

The OFT has produced a booklet setting out how an APR should be calculated. Download Credit Charges and APR (pdf 238 kb).

Not exactly light reading though. Or quick maths.

TrickyDicky

I cheated - I used a loan calculation spreadsheet. But I get the APR to be 22.7%

I think that prudent minds one might be a bit wrong - Ive tried 2 difference sources to get 22.7%

http://www.moneymadeclear.fsa.gov.uk/tools.aspx?Tool=loan_calculator
and also a spreadsheet from https://www.vertex42.com (its in $s, but its a nice comprehensive spreadsheet. It allows you to add additional payments in any given month.

NickX

Thanks for the link and I appreciate your speedy response.

However, this is what we did in the other thread to get an approximate answer.

What I am looking for is the precise mathematical formula. I believe it forms an early part of the training to become an actuary and possibly an accountant.

So its the Maths gurus who I am looking for, if they are out there

sleepless_saver

The equation is in the link that another poster and I posted. Note it is one of those lovely equations where there may not be a unique solution.:D

NickX

Wow, thanks for the quick responses.

The OFT guide is exactly what I was looking for.

It is NOT an easy calculation, and I'm glad I wasn't going mad over-complicating things. I had got to the stage where I was applying logarithms and using A-level maths but it looks like thats what it needs.

Now, next time you buy a car and the salesman offers you finance, just try asking him to work out the APR for you

fermi

NickX wrote: »

What I am looking for is the precise mathematical formula.

You did ask. :p



Read page 9 onwards of: http://www.oft.gov.uk/shared_oft/consumer_leaflets/credit/oft144.pdf

NickX

fermi wrote: »

You did ask. :p

I did indeed, and I am relieved that my failure to calculate this correctly was not due to a loss of mathematical ability, and indeed it is a virtually unsolveable equation.

All the loan calculator sites will work on the basis of an "iterative solution" whereby multiple APR figures are processed until the accuracy of the result indicates a level which would indicate that the APR parameter at that point was close enough to become a published result.

However, how on earth this was done before the advent of computers is beyond me.

TimDJ

I remember calculating APRs in exams and we would do it iteratively - guess 10%, 15%, 20% and work out where the Present Value of the loan was closest to zero. Then start narrowing it down to two decimal places using Newton-Raphson or similar.

These days I'd use XIRR() in excel!