On your $60$th birthday, you withdraw $$30,000$ from your retirement saving account to pay for a vacation to Asia and use the remaining funds to buy an annuity that will pay you $3,\frac{000}{?}$ month for $20$ years with the first payment starting one month after your $60$ th birthday. Assume you earn $4\%$ compounded monthly the entire time. How much did you have in your retirement account on your $60$th birthday?

A$)$ $$526,715\mathrm{.}79$

B$)$ $$525,065\mathrm{.}57$

C$)$ $$466,715\mathrm{.}79$

D$)$ $$1,137,001\mathrm{.}34$

E$)$ $$465,065\mathrm{.}57$