Miranda has $1000 to invest. She has narrowed her options to two four-year certificates: A and B. Certificate A pays interest at 8% p.a. compounded semi-annually the first year, 8% p.a. compounded quarterly the second year, 8% p.a. compounded monthly the third year, and 8% p.a. compounded daily the fourth year. Certificate B pays 8% p.a. compounded daily the first year, 8% p.a. com- pounded monthly the second year, 8% p.a. compounded quarterly the third year, and 8% p.a. compounded semi-annually the fourth year.
(a) What is the value of each certificate at the end of the four years?
(b) How do the values of certificates A and B compare with the value of a third certificate that pays interest at 7% compounded daily for the full four-year term?