Congratulations! You just won the Oz Lotto prize.The amount awarded is paid in 20 equal annual installments,at the beginning of each year.You can invest your money at 6.6%,compounded annually.You have calculated that the lottery is worth $20,975,400 today.How much was the amount awarded?

Question

Quizplus · Accepted Answer

Since the lottery prize is paid in 20 annual installments and we have been given the present value (PV) of the lottery, we can use the present value formula to find the amount of each installment.

PV = (PMT / r) x [1 - (1 + r) ^ -n]

Where PV = 20,975,400, r = 6.6%, and n = 20.

Plugging in the values, we get:
20,975,400 = (PMT / 0.066) x [1 - (1 + 0.066) ^ -20]

Solving for PMT, we get:
PMT = $1,727,871

Therefore, each annual installment is $1,727,871. To find the total amount awarded, we simply multiply this amount by the number of installments, i.e., 20.

Total amount awarded = $1,727,871 x 20 = $34,557,420

Therefore, the correct answer is Option B) $36,000,000 (rounded to the nearest million)

Congratulations! You Just Won the Oz Lotto Prize