Value of an annuity versus a single amount

Personal Finance Problem

Assume 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 30 years? (that is, ?$1 560,000 over 30?years) 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 30 ?years? 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.