Value of an annuity versus a single amountPersonal Finance ProblemAssume that you just won the state lottery. Your prize can be taken either in the form of $52,000 at the end of each of the next 30years (that is, $1 560,000 over 30years) or as a single amount of $867,000 paid immediately.

a. If you expect to be able to earn 8% annually on your investments over the next 30

years, ignoring taxes and other considerations, which alternative should you take? Why?

b. Would your decision in part a change if you could earn 10% rather than 8% on your investments over the next

30years? Why?

c. On a strictly economic basis, at approximately what earnings rate would you be indifferent between the two plans?

a. To decide which alternative to take, you need to compare the values of these alternatives. Although the total nominal dollar amount of the annuity is much larger than the single payment, the former is not necessarily a better choice due to the different timing of cash flows. A way to make a meaningful comparison of the two alternatives is to compare their present values.

If you take the prize as an annuity, the present value of the 30-year ordinary annuity is $585405

. If you take the prize as a single amount, the present value of the lump sum is $802780

Which alternative should be chosen?(Select the best answer below.)

Annual payments, because the present value is greater. Lump sum ,

because the present value is greater.Your answer is correct.

b. If you earned 10% rather than 8% on your investments, the present value of the 30-year ordinary annuity is $490200

Which alternative should be chosen?(Select the best answer below.)Lump sum

because the present value is greater.Your answer is correct.

Annual payments, because the present value is greater.

c. On a strictly economic basis, the rate at which you would be indifferent between the two plans is $________%.

(Round to two decimal places.)

Enter your answer in the answer box and then click Check Answer.