Value of an annulty 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 $58,000 at the end of each of the next 30 years that is $1,500,000 over 30 years) or as a single amount of $1,067,000 paid immediately a. If you expect to earn 5% annually on your investments over the next 30 years, ignoring taxes and other considerations, which aterative should you take? Why? b. Would your decision in part a change you could earn 7% rather than 5% on your investments over the next 30 years? Why? c. At approximately what interest rate would you be Indifferent between the two options? - To decide which womative to take, you need to compare the values of these alternatives. Although the total nominal dolar amount of the annually a much larger than the single payment, the former is not necessarily a beter choice due to the different timing of cash flows. A way to make a meaningful comparison of the two alteratives is to compare their present values If you take the prize as an annuity, the present value of the 30-year ordinary nuity is $(Round to the nearest cent.) you take the price as a single amount, the present value of the lump sum is (Round to the nearest dolar) Which alternative should be chosen? (Select the best answer below) O Annual payments, because the present value is greater Lumpsum, because the present value is greater b. If you earned 7. rather than 5% on your investments, the present value of the 30-year ordinary annuity is $(Round to the nearest cent) Which leative should be chosen? (Select the best answer below) Annual payments, because the present value is greater Lumpsum, because the present value is greater c. On a strictly economie basis, the rate at which you would be indifferent between the two plans is Round to two decimal places.)