Question

On January 1, you win $50,000,000 in the state lottery. The $50,000,000 prize will be paid in equal installments of $6,250,000 over 8 years. The payments will be made on December 31 of each year, beginning on December 31 of this year. If the current interest rate is 5%, determine the present value of your winnings. Use the present value tables in Exhibit 7. Round to the nearest whole dollar.

Answer 1

The present value of the winnings is $40,709,063.

Step-by-step explanation:

To determine the present value of the winnings, we need to calculate the present value of each installment of $6,250,000 using the present value formula.

The present value formula is:

PV = Payment / (1 + Interest rate)t

Where PV is the present value, Payment is the payment amount, Interest rate is the interest rate, and t is the number of years.

Using this formula, we can calculate the present value of each installment and add them up to get the total present value of the winnings.

Here is the calculation:

1. First Year Payment: PV = $6,250,000 / (1 + 0.05)1 = $5,952,381
2. Second Year Payment: PV = $6,250,000 / (1 + 0.05)2 = $5,684,992
3. Third Year Payment: PV = $6,250,000 / (1 + 0.05)3 = $5,428,086
4. Fourth Year Payment: PV = $6,250,000 / (1 + 0.05)4 = $5,181,987
5. Fifth Year Payment: PV = $6,250,000 / (1 + 0.05)5 = $4,946,068
6. Sixth Year Payment: PV = $6,250,000 / (1 + 0.05)6 = $4,719,780
7. Seventh Year Payment: PV = $6,250,000 / (1 + 0.05)7 = $4,502,625
8. Eighth Year Payment: PV = $6,250,000 / (1 + 0.05)8 = $4,294,144
9. Total Present Value: $5,952,381 + $5,684,992 + $5,428,086 + $5,181,987 + $4,946,068 + $4,719,780 + $4,502,625 + $4,294,144 = $40,709,063

Therefore, the present value of your winnings is $40,709,063.