Two accounts have a nominal rate of $8\mathrm{.}87\%$ but are compounded differently.

a$.$ Find the effective rate of an account if the balance is $Q=1600(1+\frac{0\mathrm{.}0887}{4}{)}^{4t},$ when there is a nominal rate of $8\mathrm{.}87\%$ compounded quarterly.

b$.$ Find the effective rate of an account if the balance is $Q=1600e^{0\mathrm{.}0887t},$ when there is a nominal rate of $8\mathrm{.}87\%$ compounded continuously.

a$.$ First solve the equation $1600b^t=1600(1+\frac{0\mathrm{.}0887}{4}{)}^{4t},$ where $t$ is in years. $1600(,{)}^t=1600(1+\frac{0\mathrm{.}0887}{4}{)}^{4t}$

$($Round to four decimal places as needed.$)$

The effective rate is $\%.($Round to two decimal places as needed.$)$

b$.$ First solve the equation $1600b^t=1600e^{0\mathrm{.}0887t},$ where $t$ is in years. $1600(,{)}^t=1600e^{0\mathrm{.}0887t}$

$($Round to four decimal places as needed.$)$

The effective rate is $\%.($Round to two decimal places as needed.$)$