Suppose a state lottery prize of $2 million is to be paid in 20 payments of $100,000 each at the end of each of the next 20 years. If money is worth 9%, compounded annually, what is the present value of the prize?

To find the present value of the lottery prize, we need to calculate the value of each payment at today's dollars and then sum them up.

The formula to calculate the present value of an annuity is given by:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:
PV = Present Value
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods

In this case, the payment per period (PMT) is $100,000, the interest rate (r) is 9% or 0.09, and the number of periods (n) is 20.

Let's plug these values into the formula and calculate the present value (PV):

PV = $100,000 * [(1 - (1 + 0.09)^-20) / 0.09]

Calculating this expression, we find:

PV ≈ $100,000 * (1 - 0.145) / 0.09
PV ≈ $100,000 * 0.855 / 0.09
PV ≈ $855,000 / 0.09
PV ≈ $9,500,000

Therefore, the present value of the $2 million prize is approximately $9,500,000.