You just inherited $3 million from your aunt. You decide to pursue a career as a

Question

You just inherited $3 million from your aunt. You decide to pursue a career as an artist after graduation and would like to make your inheritance last until you become a critical success. You want to convert the $3 million dollars into an annuity that will make annual payments for 40 years beginning one year from today.



(a) You would like to receive 40 equal nominal dollar payments each year beginning one year from today. Assuming a 4% nominal interest rate what annual payment (in nominal dollars) can you expect? $151,570.47

(b) You read that inflation in the U.S. is 3% per year. If you want the annual annuity payments to preserve your purchasing power over the next 40 years, how much should your annual payment be in today

Explanation / Answer

We have Present Value PV = $3M, nper = No of periods = 40, Future Value FV =0 a. Rate = 4%. So ANnual Annuity Payment PMT = PMT(Rate,nper,PV,FV) ie PMT = PMT(4%,40,3000000,0) = -$151,570.47 ......................Ans(a) (-) sign indicates that this is a Cash Outflow. b. Nominal Int Rate = 4%. Inflation 3%. So Net Int rate = 4%-3% =1% = Rate So ANnual Annuity Payment PMT = PMT(Rate,nper,PV,FV) ie PMT = PMT(1%,40,3000000,0) = $90,462.17 ......................Ans(b) (-) sign indicates that this is a Cash Outflow.

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