Judy Bright has just won the lottery.She can elect to receive her winnings in equal payments of $200,000 a year for the next ten years on December 31 or to receive $2,000,000 immediately.If the current interest rate is 6%,which choice will provide the highest amount:
A)Receiving $2,000,000 immediately.
B)Taking equal payments for 10 years.
C)It does not matter since either choice provides the same amount.
D)Refusing to accept the winnings since it is not enough.

Question

Quizplus · Accepted Answer

To compare the two options, we need to calculate the present value of the equal payments for 10 years. Using the formula for the present value of an annuity, we get:

PV = Payment x (1 - 1 / (1 + r)^n) / r

where PV is the present value, Payment is the annual payment, r is the interest rate, and n is the number of periods. In this case, Payment = $200,000, r = 6%, and n = 10. Plugging in these values, we get:

PV = $200,000 x (1 - 1 / (1 + 0.06)^10) / 0.06 = $1,469,328.46

This means that the present value of the equal payments is about $1.47 million, which is less than the $2 million offered for immediate payment. Therefore, the best choice is to take the $2 million immediately.

Judy Bright Has Just Won the Lottery