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mezya [45]
3 years ago
13

Question text You have just won the lottery. The Lottery Corporation offers you two options: 1. a lump-sum payment of $400,000,

or 2. an annuity of $800,000 to be received in equal installments over the next 20 years. At what interest rate, r, will you be indifferent between the two options?
Mathematics
1 answer:
igomit [66]3 years ago
6 0
Use present value equation.
If present value of annuity equals 400,000, then you are indifferent.

PV = A(v + v^2 + ...v^{20}) \\  \\ PV = A\frac{v(1-v^{20})}{1-v}

where v = 1/(1+r) and  A = annual payment = 800,000/20 = 40,000

PV = 400,000
After subbing in the numbers, the equation is:
10 = \frac{v(1-v^{20})}{1-v} \\  \\ 10 - 10v = v - v^{21} \\  \\ v^{21} - 11v+10 = 0 \\  \\ v = 0.928034 \\  \\ \frac{1}{1+r} = 0.928034 \\  \\ r = 0.0775

Therefore at interest rate of about 7.75% you are indifferent.
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