 # Beginning vs. End Payments

An individual deposits \$10,000 at the beginning of each of the next 10 years, starting today, into an account paying 9 percent interest compounded annually. The amount of money in the account at the end of 10 years will be closest to: A. \$109,000. B. \$143,200. C. \$151,900. D. \$165,600. I know how to get the correct answer for this problem (change to beginning of period payments and solve for FV). However, I don’t understand why you don’t get the same answer if you input N=9, I=9, PV=-10k, PMT=-10k, CPT FV= 151,900. When you solve correctly, you change to begin and input N=10, I=9, PV=0, PMT=-10k, CPT FV=165,600. Why don’t you get the same FV for these two sets of entries? How is a PV=-10k any different from a due payment of 10k in period 1? Hope this makes sense to somebody. Thanks.

When you put in n=9, it’s getting the FV at the end of year 9 instead of year 10.

think of it as paying 10000 per year for 10 years. This is the normal mode. Now since you paid the amount at the beginning of period - you are earning interest @ 9 % for 1 more year. So if you did N=10, I/Y=9, PMT=10000 CPT FV --> you get -151929.30 Now your answer is: * 1.09 = 165602.93 --> Choice D. You earn interest for 1 extra period, and not as you said for 1 period less.

I understand how to correctly answer the problem, but I still don’t understand how a PV of 10k is not the same thing as a payment of 10k at the beginning of year 1. I guess it’s one of those problems I need someone to illustrate for me. Thanks for the help.

I’ll give it another go, let me know if you get it. The question asks for the FV at the END of year 10 with the 10 payments coming at the beginning of each of those years starting today. So when your inputs are like this in END mode: PV = -10000

Or just do the damn thing in BGN mode lol

JayZilla - The last part of your explanation was perfect. Now that I see it as the FV + the one extra year of interest, I understand. Thanks again.