Mathematics: 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?

Question text you have just won the lottery. the

Ответ:

Jasten

14.01.2022

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.