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.
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.
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 (http://www.oft.gov.uk/shared_oft/consumer_leaflets/credit/oft144.pdf)) .
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 (http://www.oft.gov.uk/shared_oft/consumer_leaflets/credit/oft144.pdf) (pdf 238 kb).Not exactly light reading though. ;) Or quick maths.
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 www.vertex42.com (its in $s, but its a nice comprehensive spreadsheet. It allows you to add additional payments in any given month.
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 :confused:
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
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 ;)
What I am looking for is the precise mathematical formula.
You did ask. :p:p
http://i38.tinypic.com/2n0q1bd.png
Read page 9 onwards of: http://www.oft.gov.uk/shared_oft/consumer_leaflets/credit/oft144.pdf
You did ask. :p: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.
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!
http://i38.tinypic.com/2n0q1bd.png
Thanks Fermi,
I had actually got to this on my back of an envolope working, but was trying to manipulate the algebra to get a formula for i (Rate of Interest).
I had tried calculus and logs and exponents, but was just getting confused.
Looks like the iterative solution is the only way.
If it's just the figures you stated (i.e no upfront charge for finance etc.), and the interest is payable from day one, then the interest rate is 23.63%.
If interest is payable monthly in arrears, then the rate is 22.67%.
Please note that there is NO formula for yield (i.e. interest). These answers are achieved by "iteration".
Please note that there is NO formula for yield (i.e. interest). These answers are achieved by "iteration".
Thanks, I think that is the conclusion being reached. Iteration is the only way.
However, I think given the APR, the amount of the Loan and the Monthly Repayment, it is possible to work out precisely how many payments would be required.
wow...that looks like fun...was wondering what to do with my weekend!
so much light reading...!
However, how on earth this was done before the advent of computers is beyond me.
I don't think it was done. The only real value of the APR is as a value to compare different products - its a regulatory requirement rather than a business one.
NickX, there IS a formula for TERM, but this assumes that you know your yield i.e APR.
What exactly is your objective? Are you trying to compare different loan offers or just calculate an APR? If it's the latter, then surely it would just be better to look at the monthly repayment? I say this only because APR's as about as useful as a fart in a spacesuit! They have been designed by intellectuals who seem to have no idea about what happens in the real world.
Good luck with your quest!
NickX, there IS a formula for TERM, but this assumes that you know your yield i.e APR.
What exactly is your objective? Are you trying to compare different loan offers or just calculate an APR?
LOL well my objective was just to refresh my mind on the mathematics behind APR and loan calculations. I am sure I did it when studying A-level Statistics, but that was **cough** **cough** 20 years ago ;)
I have worked out the formula for the TERM on the basis that you know the yield, the Total Amount borrowed and the monthly Payment. It still uses logarithms though, so specialist knowledge is required.
I'm not quite sad enough to dig out any old textbooks just yet.
But yes, it just goes to prove how much use theoretical algebra is in the real world ;)
Thanks for everyone's input anyway.
NickX, have you got access to MS Office? All of the formulae you need are on there. Failing that Open Office will do.
But I suspect that you are more interested in enjoying the Maths, which is cool.
Also, have you thought about buying a financial calculator? You can get some good ones from Hewlett Packard AND, of course, the the instruction manuals have the formulae in them.
Good luck!
What exactly is your objective?This has got nothing to do with stoozing beer money again has it Nick? :rolleyes:
This has got nothing to do with stoozing beer money again has it Nick? :rolleyes:
LOL No, but once you have spent some time on this, the beer becomes a very attractive alternative pastime ;)
NickX, have you got access to MS Office? All of the formulae you need are on there. Failing that Open Office will do.
But I suspect that you are more interested in enjoying the Maths, which is cool.
Thanks, will have a look at MS Office (probably tomorrow now).
And yes my interest was more of the actual maths than anything practical.
However LongTermLurker has reminded me that it is in danger of digging into valuable drinking time, so perhaps I'll pick up on this another time.
However LongTermLurker has reminded me that it is in danger of digging into valuable drinking time, so perhaps I'll pick up on this another time.
LOL, it's all about priorities ;)
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