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 $53,000 at the end of each of the next 30 years (that is, $1,590,000 over 30 years) or as a single amount of $687,000 paid immediately.

a. If you expect to earn 11% 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 13% rather than 11% on your investments over the next 30 years? Why?

c. At approximately what interest rate would you be indifferent between the two options?

Compounding frequency, time value, and effective annual ratesFor each of the cases in the following table,

Case	Amount of initial deposit		Nominal annual rate, r		Compounding frequency, m (times/year)	Deposit period (years)
A	$2,600		6%		2	5
B	$52,000		14%		6	3
C	$900		7%		2	12
D	$20,000		14%		4	6

a.Calculate the future value at the end of the specified deposit period.

b.Determine the effective annual rate, EAR.

c.Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship exists between compounding frequency and the nominal and effective annual rates?