Janet Boyle intends to deposit $$$$340$ per year in a credit union for the next $5$years$,$ and the credit union pays an annual interest rate of $7\%.$ a$.$Determine the future value that Janet will have in $5$years$,$ given that$$ end$-$of$-$period deposits are made and no interest is$$ withdrawn, if

$(1)$$$340$ is deposited annually and the credit union pays interest annually.

$(2)$$$170$ is deposited semiannually and the credit union pays interest semiannually.

$(3)$$$85$ is deposited quarterly and the credit union pays interest quarterly. b$.$Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.