A state lottery commission pays the winner of the "Million Dollar" lottery 20 annual installments of $30,000 each. If the prevailing interest rate is 8% /year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar.
A) $301,432
B) $294,968
C) $299,289
D) $300,523

Question

A state lottery commission pays the winner of the "Million Dollar" lottery 20 annual installments of $30,000 each. If the prevailing interest rate is 8% /year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar. ​
A) $301,432
B) $294,968
C) $299,289
D) $300,523

Quizplus · Accepted Answer

The present value of an annuity can be calculated using the formula for the present value of a series of cash flows. Given the continuous compounding interest rate, the formula is: PV = Pmt * (1 - e^(-rt)) / r. Here, Pmt = $30,000, r = 0.08, and t = 20. Plugging in these values gives the present value closest to $299,289.

A State Lottery Commission Pays the Winner of the "Million