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I used a loan calculator which gives an effective rate of 80.781 whereas wikipedia http://en.wikipedia.org/wiki/Annual_percentage_rate gives a rate of 49% for these parameters:

  • borrowed: 100
  • fees: 10
  • rate: 5% per month (60% per year)

amortization table is:

t1 -> 5.50 6.91 103.09

t2 -> 5.15 7.26 95.83

etc.

The rate of wikipedia is much lower than the annual nominal rate of 60% so it's misleading the consumer somehow whereas 80.80 seems closer to reflect this costfull loan.

I don't care about who is right or wrong, I know how wikipedia calculates its rate, I cannot find out how the software calculates it. So my question is: can you deduce their formula ? Excel function equivalents would be fine for the answer.

  • What kind of calculator are you using to get the 80.781? Is it an online tool? Can you link to it? – Chris W. Rea Mar 11 '12 at 13:11
  • Wikipedia says (see the section on Multiple definitions odf APR) that a $100 loan plus $10 fee plus 5% interest per month that is paid off in full at the end of one month (payment = $115) has an annual percentage rate of 1.05^{12} - 1 = 79.58% according to one definition of APR, and an APR of 1.15^{12}-1 = 435% according to another definition of APR. It depends on whether the fee is included in the calculation or not. The former is pretty close to what your loan calculator gave you. Maybe your calculator assumes the $10 is paid up front or at the end of the first month? – Dilip Sarwate Mar 11 '12 at 13:36
  • Please give link of the calculator. I could not find it on the wikipedia page. – Natwar Lath Mar 11 '12 at 14:09
  • What is the payment or number of periods? One or the other is needed to finish the calculation. – JoeTaxpayer Mar 11 '12 at 18:40
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First - it's a different process for anyone to answer a straight question than to try to figure out someone else's potentially wrong answer.

A nominal 60% will result in an APR of 79.6%, regardless of the numbers involved.

You show the beginning of an amortization table that is written as if one borrowed $110, and paid it back over 12 months or so it appears to me. This is not how I'd create the APR for the scenario you propose. Present value of $90, but use the payment on the full $100. Or if you actually get the $100 but owe $110, then use the payment on the $110 but PV of $100. This should bring the monthly rate to 8.74% from 5%.

If this isn't clear, ask a follow up and I'll edit response.

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