Question

You pay the present value of $1000 now to receive $25 at the end of each...

You pay the present value of $1000 now to receive $25 at the end of each month over the next 5-year period. At the end of 5 years, the investor will also receive a windfall of $500. What is the annual interest rate of your investment? (Show all work for any credit)

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Answer #1
We have the equality
1000 = 25*PVIFA(r,60)+500*PVIF(r,60), where
r = the interest rate per month.
This has to be found out by trial and error so that
the value of RHS in the above equation is 1000
Discounting with 2%
= 25*34.76089+500*0.30478 = $    1,021.41
Discounting with 3%
= 25*27.67556+500*0.16973 = $       776.75
r lies between 2% and 3%.
By simple interpolation r = 2%+1%*21.41/(1021.41-776.75) = 2.08751%
Annual interest rate = 2.08751*12 = 25.05%
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