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

3.44%

Step-by-step 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=(A(1-(1+r)^(-n) ))/(r)`

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

n = 20 years

`15,000,000=(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%.