I'm currently working on a homework problem where you lend a friend $40k and they pay you back in "6 equal annual installments commencing in exactly one year". What's tricky about this question is I need to figure out the amount of the annual payments with an interest rate of 8.0% p.a. compounded monthly, and I don't really know what to do.

I tried using the present value of annuities, rearranging to solve for cash flow, and then plugging in all my variables. But I especially was unsure what to do with the number of payments (exponent 'n' in the EAR). I would think it should be 6 because my friend is only making 6 payments, but since I divide 'i' by 12 due to the compounded monthly bit I should have to multiply 6 by 12. Except that goes against what the problem say's of only making 6 payments. I've tried both ways ('n=6, n=72') and neither worked. I also thought that by doing 'n=72', this would be the price my friend would pay if he was doing monthly installments so I tried multiplying that by 12 (to equal how much he'd pay per year) but that didn't work either.

What am I missing with this question?


1 Answer 1


You simply need to find the "effective annual interest rate", since the compounding rate for the payments is one year. The compounding period must equal the payment period for the regular payment formulae to work.

So just take the nominal annual rate , 8% compounded monthly, and turn it into a monthly rate, by dividing by 12.

Then take this monthly rate, and compounded it 12 time to get the effective annual rate.

So the new effective annual rate is just:

I=(1+.08/12)^12 - 1

Now use this rate with 6 annual payments...

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