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APR Calculations


Following on from a question yesterday I am looking at an online finance calculator on behalf of a customer


And they are insisting that the APR calculated by this calculator is correct. However it does not give an answer comparable to any other online calculators

For example on a loan of 10000 at 7% interest paid over 36 months this give an APR of 13.6%. Other online calculators give a value half this.

Do any of you math whizzes have any idea why this calculator gives such different values and what formula is uses. I obviously don't understand enough about APR to know why this vastly different value is correct and I don't want to look stupid to my customer :(

Thanks a lot
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1 Solution
They are using this formula here

If I plug in the numbers there except they use t1 = 0 for the left side and t1=1 for the right side

Left side of the equation is just total loan amount
10000 = SUM(k=1 to M) of (P_k*(1+APR/100)^(-T_k)
Where M is number of payments, P_k is payment number k, and T_k is the time that has passed since the loan started (in years).

If I plug in 11.457 for the ARP, the equation works out perfectly if I use T_1 = 1/12, T_2 = 2/13 etc.
It also works for any other combination I tried.
The Wikipedia article says T_1=0 though.
Note that it agrees with the calucator here:


The only thing is that the weird way they compute the interest makes it confusing. Note that the interest rate is not part of the calculation, just the payments and the term.
So to get the payment the same in the new calculator, use 10.895 as the rate and you will see the APR matches (11.46)

Note that they also try to tell you how to calculate the APR in Excel, although they don't really give the formula
It should be clear now that APR means different things in different regions. If you live in the European Union, then they have laws about how APR is defined. The APR on the calculator in question and the EU APR in the calculator I just mentioned match and also are confirmed on my spreadsheet. The Wikipedia article saying T_1 = 0 must be using T_1 for the downpayment, so the first actual payment would be T_2 = 1/12 and thus everything agrees.

The other calculators that give different APRs are using the common U.S. definition of APR. The nice thing about the calculator I just posted is that it gives both.
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andiejeAuthor Commented:
Thanks a lot for your help
andiejeAuthor Commented:
By the way, what did you use to 'plug in the numbers'
Did you knock the answer up in a programming language or did you use excel?
thanks a lot
andiejeAuthor Commented:
Also, is this a typo in this comment: ID: 39732082
T_2 = 2/13 etc.
andiejeAuthor Commented:
Thanks a lot. In case you are interested I managed to get a reply of the software authors and they concurred with your deductions. Thanks for saving me some time!
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