Calculate the following: $(LG15-2$

a$.$ What is the amount of the annuity purchase required if you wish to receive a fixed payment of $$200,000$ for $20$ years? Assume that the annuity will earn $6$ percent per year.

b$.$ Calculate the annual cash flows $($annuity payments$)$ from a fixed$-$payment annuity if the present value of the $20-$year annuity is $$1$ million and the annuity earns a guaranteed annual return of $6$ percent. The payments are to begin at the end of the current year.