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 $37,000 at the end of each of the next 20 years (that is, $740,000 over 20 years) or as a single amount of $508,000 paid immediately.

a. If you expect to earn 7% annually on your investment over the next 20 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 20 years? Why?

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