Annuities and compounding$$Personal Finance Problem$$Janet Boyle intends to deposit $$$$240$ per year in a credit union for the next $5$years$,$ and the credit union pays an annual interest rate of $8\%.$

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future value that Janet will have in $5$years$,$ given that$$ end$-$of$-$period deposits are made and no interest is$$ withdrawn, if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)$$$240$ is deposited annually and the credit union pays interest annually.

$(2)$$$120$ is deposited semiannually and the credit union pays interest semiannually.

$(3)$$$60$ 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.

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Part $1$

a$.(1)$ If $$$$240$ is deposited annually and the credit union pays interest$$ annually, the future value that Janet will have at the end of $5$ years is $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$