Question

ebookprint item question content area present value of an annuity on january 1 you win $4,400,000 in the state lottery. the $4,400,000 prize will be paid in equal installments of $440,000 over 10 years. the payments will be made on december 31 of each year, beginning on december 31. if the current interest rate is 8%, determine the present value of your winnings. use the present value tables in exhibit 7. round to the nearest whole dollar. $fill in the blank 1

Answer 1

The present value of the lottery winnings is $2,498,866. Round to the nearest whole dollar, this is $2,498,000.

To determine the present value of the lottery winnings, we need to calculate the present value of each annual payment of $440,000 and then sum them up.

Assuming an interest rate of 8%, the present value of the first payment of $440,000 on December 31 is $400,872. This is determined by looking up the present value of an ordinary annuity of $1 for 10 periods at 8% in the present value tables (Exhibit 7), which is 0.693. We can then multiply this value by the annual payment amount of $440,000 to get the present value of the first payment.

The present value of the remaining payments can be calculated in the same way, using the present value of an ordinary annuity of $1 for 9 periods at 8%, which is 0.621. Thus, the present value of each of the remaining payments is $400,872 * 0.621 = $249,995.

Summing up the present value of all 10 payments, we get $400,872 + $249,995 + $249,995 + ... + $249,995 = $2,498,866.

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