Present Value of 1 Future Value of 1 Present Value of an Annuity of 1 Future Value of an Annuity of 1 Sheryl Frasier has won the Indiana state lottery when the jackpot was $9 million. She has chosen to take the prize winnings as $1 million per year over the next nine years. Using a 7% annual interest rate, determine the present value of the $1 million annuity Sheryl will receive.
A)$9,000,000
B)$8,370,000
C)$6,515,200
D)$5,670,000
E)$4,895,100

Question

Present Value of 1  Future Value of 1  Present Value of an Annuity of 1  Future Value of an Annuity of 1  Sheryl Frasier has won the Indiana state lottery when the jackpot was $9 million. She has chosen to take the prize winnings as $1 million per year over the next nine years. Using a 7% annual interest rate, determine the present value of the $1 million annuity Sheryl will receive.
A)$9,000,000 
B)$8,370,000 
C)$6,515,200 
D)$5,670,000 
E)$4,895,100

Quizplus · Accepted Answer

To find the present value of the annuity, we need to use the formula:

Present Value of Annuity = Payment x (1 - (1 + r)^-n) / r

where r is the interest rate per period (in this case, 7% per year), n is the number of periods (in this case, 9 years), and Payment is the annual payment received (in this case, $1 million).

Plugging in the numbers, we get:

Present Value of Annuity = $1,000,000 x (1 - (1 + 0.07)^-9) / 0.07

= $1,000,000 x (1 - 0.5084) / 0.07

= $6,515,200

Therefore, the answer is C, $6,515,200.