Question

You win a lottery that claims to pay a prize of $1 million in the form of a payment of $50,000 at the end of each year for the next twenty years. What is the real value of the prize if the interest rate is 14 percent?

Answer 1

To calculate the present value of a lottery prize of $1 million paid over twenty years at a 14% interest rate, we use the present value of an annuity formula. This calculation will yield the real value of the prize, which will be less than $1 million.

Step-by-step explanation:

To determine the real value of a lottery prize of $1 million paid as $50,000 at the end of each year for twenty years with an interest rate of 14 percent, we need to calculate the present value of an annuity. The present value of an annuity can be found using the formula:

PV = Pmt × [(1 - (1 + r)^{-n}) / r]

where:

For this question:

Plugging these values into the formula gives:

PV = $50,000 × [(1 - (1 + 0.14)^{-20}) / 0.14]

Calculating this, we find the present value, which will be less than the nominal value of $1 million due to the effect of interest rate over time. This computation will show the true economic value of the winnings today.