$5-21.$

a$.$ If she can invest money at $5$ percent compounded quarterly, how much must she invest today?

b$.$ Suppose that Morduch believes that Meals for the Homeless can put aside only $$37,500$ today to buy the new van in $3$ years. However, she thinks that she can invest the money at $7\mathrm{.}20$ percent compounded monthly. Determine if she will have the $$50,000$ she will need for the new van.

c$.$ Assuming that Morduch can put aside $$37,000$ today and needs to have $$50,000$ available in $4$ years, what interest rate must be earned? Use quarterly compounding.