Calculating APR
Discussion
Hi all,
I'm looking for some help.
I'm a mathematical chap who has a decent grasp of financial matters.
However, I cannot find, for the life of me, a clear definition of APR and how to calculate it manually.
It seems that everyone has a view, but the views seem to differ, both within countries and across countries.
Take this example....
Personal loan for £20000 (including £3000 in fees) over 3 years, 10% annual rate.
What do you think is the APR?
How are you arriving at your answer?
Sorry to be such an anorak!
I'm looking for some help.
I'm a mathematical chap who has a decent grasp of financial matters.
However, I cannot find, for the life of me, a clear definition of APR and how to calculate it manually.
It seems that everyone has a view, but the views seem to differ, both within countries and across countries.
Take this example....
Personal loan for £20000 (including £3000 in fees) over 3 years, 10% annual rate.
What do you think is the APR?
How are you arriving at your answer?
Sorry to be such an anorak!
This is the current UK standards for most loans
http://www.legislation.gov.uk/uksi/2010/1011/sched...
it stems from the EU so likely to be same across eu
http://www.legislation.gov.uk/uksi/2010/1011/sched...
it stems from the EU so likely to be same across eu
Thanks.
I'm aware of this, but it's way over the top for what I'm asking, being a mathematical generalisation of a fairly simple idea.
I'm curious to see what you think the answers to my questions are, without resorting to APR calculators etc
I'm not taking the piss here and don't wish to come over as a pompous ass!!
I'm aware of this, but it's way over the top for what I'm asking, being a mathematical generalisation of a fairly simple idea.
I'm curious to see what you think the answers to my questions are, without resorting to APR calculators etc
I'm not taking the piss here and don't wish to come over as a pompous ass!!
I spent quite a bit of time earlier this year rewriting an APR calculation program - most people who looked at it said it couldn't be done but they didn't understand the mathematics behind it.
My code allowed for a maximum of 30 iterations to calculate the internal rate of return to the necessary accuracy - you can't calculate APR with a nice simple equation due to the need to resolve the summation of terms involving powers to be 0. All good fun
My code allowed for a maximum of 30 iterations to calculate the internal rate of return to the necessary accuracy - you can't calculate APR with a nice simple equation due to the need to resolve the summation of terms involving powers to be 0. All good fun
Simpo Two said:
Amusing to see that the standard way to express interest rates, which affect us all, is in a way that nobody can understand still less calculate. What numbnut thought that up then?
Its a complex calculation and will always be one - so it cannot be simplified. Its a one fits approach to COMAPRE THE COST OF CREDIT. Contrary to what many people think its not an interest per se because it includes all of the costs not just the annual interest cost.Its designed to allow you to compare the overall cost of credit - not just interest rate which is just 1 factor.
Don't think tis a big deal that the average person cannot work it out.
Mojooo said:
Simpo Two said:
Amusing to see that the standard way to express interest rates, which affect us all, is in a way that nobody can understand still less calculate. What numbnut thought that up then?
Its a complex calculation and will always be one - so it cannot be simplified. Its a one fits approach to COMAPRE THE COST OF CREDIT. Contrary to what many people think its not an interest per se because it includes all of the costsPerhaps then a similar thing should be applied to pensions... as people are suddenly realising that their precious retirement fund will actually pay them 4p a year. Sorry, rambling.
And here's how I get there.
£17,000 borrowed. Initial fees of £3,000. Simple interest of 10% pa.
So total amount repaid of £25,100 (i.e. £17,000 + £3,000 + 3 x 10% x £17,000)
25,100 / 3 = 8,366.67 (annual repayments - i.e. equal monthly amounts of £697.22pm in arrears)
Solve for the rate of interest such that 8,366.67 x a3(12) = 17,000. (Apologies, don't know how to do the right subscripts and superscripts on PH).
Where a3(12) = (1-v^3)/i12
and v = 1/(1+i)
and i12 = (1 + i/12)^12 - 1
I cheated and used Solver to solve that, but I think you should be able to rejig the equation to solve for i without having to use Solver.
Fair chance I've ballsed up somewhere in there but the answer feels about right given the amount borrowed, the amount paid back, and the term of the loan.
£17,000 borrowed. Initial fees of £3,000. Simple interest of 10% pa.
So total amount repaid of £25,100 (i.e. £17,000 + £3,000 + 3 x 10% x £17,000)
25,100 / 3 = 8,366.67 (annual repayments - i.e. equal monthly amounts of £697.22pm in arrears)
Solve for the rate of interest such that 8,366.67 x a3(12) = 17,000. (Apologies, don't know how to do the right subscripts and superscripts on PH).
Where a3(12) = (1-v^3)/i12
and v = 1/(1+i)
and i12 = (1 + i/12)^12 - 1
I cheated and used Solver to solve that, but I think you should be able to rejig the equation to solve for i without having to use Solver.
Fair chance I've ballsed up somewhere in there but the answer feels about right given the amount borrowed, the amount paid back, and the term of the loan.
Brilliant replies chaps, thanks for taking the time to write them!
Is it not the case that the total loan amount is £20K, with the effective loan being £17K?
It certainly provokes discussion and debate....check out the link below:
http://forums.moneysavingexpert.com/showthread.php...
Is it not the case that the total loan amount is £20K, with the effective loan being £17K?
It certainly provokes discussion and debate....check out the link below:
http://forums.moneysavingexpert.com/showthread.php...
I know how to calculate APR; I don't know how loans work! 
I did wonder if I had got the terms of the loan right.
Feels harsh to charge you interest on the fees as well but the good thing about APR is that it would take that into account in the calculation.
Anyway, the APR calculation is as above except that the total amount repaid is £26K as interest is levied on £20K not £17K. This increases the APR to 19.0%. (I seem to think from some exams I did - 20 years ago! - that APR is rounded to the nearest 0.1%.)
I did wonder if I had got the terms of the loan right. Feels harsh to charge you interest on the fees as well but the good thing about APR is that it would take that into account in the calculation.
Anyway, the APR calculation is as above except that the total amount repaid is £26K as interest is levied on £20K not £17K. This increases the APR to 19.0%. (I seem to think from some exams I did - 20 years ago! - that APR is rounded to the nearest 0.1%.)
Zigster said:
I know how to calculate APR; I don't know how loans work! I did wonder if I had got the terms of the loan right.
Feels harsh to charge you interest on the fees as well but the good thing about APR is that it would take that into account in the calculation.
Anyway, the APR calculation is as above except that the total amount repaid is £26K as interest is levied on £20K not £17K. This increases the APR to 19.0%. (I seem to think from some exams I did - 20 years ago! - that APR is rounded to the nearest 0.1%.)
And that's not right either! D) The £3K initial fee is paid back immediately rather than over 3 years so allowing for that would push the APR higher. I did wonder if I had got the terms of the loan right. Feels harsh to charge you interest on the fees as well but the good thing about APR is that it would take that into account in the calculation.
Anyway, the APR calculation is as above except that the total amount repaid is £26K as interest is levied on £20K not £17K. This increases the APR to 19.0%. (I seem to think from some exams I did - 20 years ago! - that APR is rounded to the nearest 0.1%.)
Simpo Two said:
Yes, I agree it is for comparative purposes.
Perhaps then a similar thing should be applied to pensions... as people are suddenly realising that their precious retirement fund will actually pay them 4p a year. Sorry, rambling.
You think that pensions DON'T work on the basis of compound interest (which is effectively what APR is designed to show)...!!Perhaps then a similar thing should be applied to pensions... as people are suddenly realising that their precious retirement fund will actually pay them 4p a year. Sorry, rambling.
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