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 $${39}^{\text{'}},000$ at the end of each of the next $20$ years $($that is$,$ $$780,000$ over $20$ years$)$ or as a single amount of $$536,000$ paid immediately.

a$.$ If you expect to earn $7\%$ annually on your investments 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?