John Doe has the opportunity to invest in either of two annuities, each of which will cost $$38,000$ today. Annuity X is an annuity due that makes six payments of $$9,000.$ Annuity Y is an ordinary annuity that makes six payments of $$10,000.$ Assume that John Doe can earn $15\%$ on his investments.

a$.$ On a purely intuitive basis $($i$.$e$.$ without doing any math$),$ which annuity do you think is more attractive? Why?

b$.$ Find the Future Value after six years for both annuities?

c$.$Use your finding in part $($b$)$ to indicate which is more attractive. Why? Compare your finding to your intuitive response in part $($a$).$