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 $$59,000$ at the end of each of the next $25$ years $($that is$,$ $$1,475,000$ over $25$ years$)$ or as a single amount of $$841,000$ paid immediately.

a$.$ If you expect to earn $7\%$ annually on your investments over the next $25$ years, ignoring taxes and other considerations, which alternative should you take? Why?

b$.$ Would your decision in part a change if you could earn $9\%$ rather than $7\%$ on your investments over the next $25$ years? Why?

c$.$ At approximatelv what interest rate would vou be indifferent between the two options?

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 $25-$year ordinary annuity is $

$($Round to the nearest cent.$)$

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

$($Round to the nearest dollar.$)$

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.

b$.$ If you earned $9\%$ rather than $7\%$ on your investments, the present value of the $25-$year ordinary annuity is $ $($Round to the nearest cent.$)$

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.

c$.$ On a strictly economic basis, the rate at which you would be indifferent between the two plans is $\%.($Round to two decimal places.$)$