3. Suppose you win the lottery and are given the following three options: (1) Re

Question

3. Suppose you win the lottery and are given the following three options: (1) Receive 20 million dollars today (2) receive 1.5 million dollars per year over the next 20 years; (3) receive 1 million dollars per year indefinitely (being passed on to your heirs). which is the best deal, assuming that the annual interest rate is 5%? We will use option 1 as the standard to compare these three options by converting options 2 and 3 into the present value (i.e. today's dollars). Consider option 2, (a) Use Pi to denote the present value of 1.5 million dollars received after n-th year. Find Pih,P, and a general formula for Pr (b) How much is the 1.5 million dollars received annually over the course of 20 years worth in terms of today's dollars? Consider option 3, (c) Use Qn to denote the present value of 1 million dollars received after n-th year. Find Q1,02, 0s and a general formula for Q (d) How much is the 1 million dollars received per year indefinitely worth in terms of today's dollars? (e) Determine which of the three options is best.

Explanation / Answer

(a) i= 5%=0.05

A = 20 [(1.05) -1 /(0.5)(1.05)]

= 20(0.9524)

=1.9047 million dollars.

(b) Given

pv=1.5

i = 20(0.05) =1

n = 20

Pn = 1.5[(2)20 -1/1(2)20

= 1.5(1048575/1048576)

=1.5 milli0n dollars

(c)Given

i=0.05

n=1

Q = 1 [(1.05)-1/0.05(1.05)]

= 0.05 /0.525

= 0.24 million dolars

Therefore 3 option is best.

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