Question

The Mega Millions claims its grand prize is $500 million, payable over 5 years at $100,000,000 per year. If the first payment is made immediately, what is this grand prize really worth today? Use an interest rate of 4%.

Answer 1

Answer:

The prize is worth $462.9895 million or 462,989,522.4 today.

Explanation:

The equal payments every period over a defined period of 5 years show that this is an annuity. The first payment is received today that is at start so it is an annuity due. We will calculate the present value of this annuity using the formula for Present value of annuity due.

Present value of Annuity due:

Using the formula, the present value is:

Present value = 100m + 100m * [(1 - (1+0.04)^-(5-1)) / 0.04]

Present value = $462.9895 million or 462,989,522.4