Suppose you invest $$200$ in a fund earning simple interest at $4\%.$ Three years later you withdraw the investment $($principal and interest$)$ and invest it in another fund earning $7\%$

simple discount. $($Round your answers to two decimal places.$)$

$($a$)$ How much time, in years, $($including the three years in the simple interest account$)$ will be required for the original $$200$ to accumulate to $$610?$

years

$($b$)$ At what annual effective rate of compound interest would $$200$ accumulate to $$610$ in the same amount of time?

$\%$