Your dreams of becoming rich have just come true. You have won the State of Tran

Question

Your dreams of becoming rich have just come true. You have won the State of Tranquility’s lottery. The state offers you two payment plans for the $5,000,000 advertised jackpot. You can take the annual payments of $250,000 for the next twenty years or $2,867,480 today.

a) If your investment rate is 8%, which payoff will you chose?

b) If your investment rate is 5%, which payoff will you choose?

c) At what investment rate will the annuity stream of $250,000 be the same as the lump-sum payment of $2,867,480?

Explanation / Answer

(A) present value of option 1 @8%=

[1-(1.08^-20)/0.08]*250000=2454536.85

It is better to take option 2as pv is greater then the option 1

(B)present value of option 1 @5%

[1-(1.05^-20)/0.05]*250000= 3115552.58

so it is better to take option 1 as the pv is greater in option 1 as compare to option 2

(c)rate at which annuity of 250000 will equal to 2867480 is i%

So required equation is

{[1-(1+i)^-20]÷i}*250000=2867480

{1-(1+i)^-20}÷i=11.47

Bg using interpolation,

i=6.06%

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