|fee  |interest(5% of 200)    |total paying   |% of original loan
|200  |6    |10                     |10+6           |8 (16/200*100)

                                    |effective loan |% of effective loan
|200  |6    |10                     |200-6          |5.154639175 *edited***(10/194*100)**

I understand the second method is what constitutes APR (figures used from http://www.diffen.com/difference/Annual_Percentage_Rate_vs_Interest_Rate) but what is wrong with using the 1st one to work out the cost of a loan?

  • You are asking about a 1 year scenario, correct? – JTP - Apologise to Monica Apr 26 '14 at 16:52
  • @JoeTaxpayer that's correct. starting with as simple as i can get – rush001 Apr 26 '14 at 18:40

The two scenarios appear to describe different loans, if you ignore the artificial designations of "fees" and "interest" and simply look at the actual cash flow.

In the first, you walk out of the lenders office with $200 to do with as you wish. One year later, you come back with $216, and everything is paid off. The payment in excess of the amount loaned ($16), as a ratio to the amount loaned ($200), is 8%

In the second, you are initially given $200, but before you get to the door, the lender reclaims his $6 fee, so you walk out the door with only $194. Still, when you come back in a year to pay off the loan, you need to pay back $210. The ratio, the same as calculated above, is $16/$194, or 8.247%

The real error is in the example cited; it's wrong. The payment of the fee is correctly converted into a reduction in the true amount loaned, but the repayment of the fee is not included in the end-of-loan repayment...

| improve this answer | |
  • Thanks for your reply. A few questions if you don't mind: Don't you think, though, that the reduction ($6) was already taken off and so shouldn't appear at end-of-loan repayment ? Also, are any of these percentages actually APR or the like, or are they just "ratios"? – rush001 Apr 26 '14 at 18:58
  • 1) I meant to say that since the fee was take off the amount of the loan before you got it, the base for counting interest at the end should be $194, not $200 – DJohnM Apr 26 '14 at 19:11
  • 2) I don't know what APR means in any particular case; it's not widely used here in Canada. Mathematically, I was trying to find a number to describe two scenarios in a way that allowed meaningful comparison. I would call the ratio I found "the effective annual interest rate" – DJohnM Apr 26 '14 at 19:18
  • RE 1), while the figure still stands, the working was incompletely/incorrectly written by me (sorry!) as having base of 200. If you work it out you'll find it to be using the base $194 all along, as NOW reflected by my edit. What is your opinion on this now? – rush001 Apr 26 '14 at 19:29
  • My problem is with the numerator; you pay back $210 on a $194 loan, so why use $10 instead of $16? Method #2 above skips the fee of 3% and so understates the effective interest rate by that same 3%. – DJohnM Apr 26 '14 at 19:48

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