Question

Your friend just won the Pennsylvanialottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What interest rate makes her indifferent between the two options

Answer 1

Answer:

3.44%

Explanation:

The interest rate that makes her indifferent is the rate that equates the present value (PV) of the annuity to $15,000,000, the amount receivable in the first choice.

$PV=\frac{A(1-(1+r)^{-n} )}{r}$

Where A = equal annual payment = $1,050,000

n = 20 years

$15,000,000=\frac{1,050,000(1-(1+r)^{-20} )}{r}$

Using a financial calculator or interpolation, the value of r that solves the equation is 3.443209% or approximately 3.44%.