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Annuity Payment N Years Away Confusion!

“An investor wants to receive $10,000 annually for ten years with the first payment five years from today. If the investor can earn a 14% annual return, the amount that she will have to invest today is closest to:”

I know how to solve the question, Enter PMT = 10,000, N = 10, and I = 14. Compute PV = 52,161.16. That is the present value of the 10-year annuity, four years from today.  But per Schweser, “Next, we need to discount that back to present for four years to find the amount of the investment today. Enter FV = −52,161.16, N = 4, I = 14, PMT = 0. Compute PV = 30,883.59.”

If the first payment is five years from today, why is N=4 and not N=5?

Thanks!

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The payments of 10K are ordinary annuities (unless the text explicitly states that it is an annuity due).

Ordinary annuities are payments made at the end of the year. And annuity due are payments made at the beginning of the year.

If your calculator is in END mode (which is most of the time unless you set it at BEG), this calculation  ”PMT = 10,000, N = 10, and I = 14” will correctly bring the cash flow at beginning of the year. So, if the first payment is made 5 years from now, the PV is at beginning of year 5 (or end of year 4).

Therefore, this PV is just brought to present for 4 years and not 5.

Las almas de todos los hombres son inmortales, pero las almas de los justos son inmortales y divinas.
Sócrates

To add to Harrogath’s (eminently correct) answer: draw yourself a timeline.  It’s invaluable in visualizing these problems and getting the correct answer.

Simplify the complicated side; don't complify the simplicated side.

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If your calculator is set to END, then the discounting is for 4 years. However, if it is set to BGN, then the discounting is for 5 years.

You could also do this problem using the C.F. worksheet.

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