Ms$.$ W is $29$ years old. She plans to retire at age $64.$ She plans to make a monthly deposit to her plension account at the end of each month from now until she retires, at age $64.$ She hopes to accumulate $$690,000$ in the account at the time of her retirement. Assuming that her pension account can generate a $7\mathrm{.}2\%$ annual interest, what should be the minimum amount of her monthly pension deposit? $($Note that over$-$rounding may give you a significant rounding error.