At the end of each quarter, a $49-$year$-$old individual puts $$1400$ in a retirement account that pays $9\mathrm{.}2\%$ interest compounded quarterly.

$($a$)$ When the individual reaches age $60,$ what is the value of the account?

$($b$)$ If no further deposits or withdrawals are made to the account, what is the value of the account when the individual reaches age $65?$

$($a$)$ Up to age $60,$ the individual's deposits form an

because the deposits are made at the

of each period. Therefore, the formula

$7$ should be used. After age $60,$ the account

to behave as an annuity and

formula should be

used.

please answer A&B$.$