$1$a$.$ You would like to open an account starting with $$600.$ You are offered $7\%$ APR and

the following choices for compounding frequency. For each choice, write a function

for the account balance after $t$ years, $b(t),$ and the annual percent yield $($APY$).$

$1$b$.$ Which compounding frequency is the best for a long$-$term account?

Consider a bank that offers a $3\mathrm{.}5\%$ APR compounded quarterly $(4$ times per year$).$

$2a.$ By what percent does this account grow after $1$ month?

Hint: $3$ months $=1$ quarter $=\frac{1}{4}$ of a year.

$2$b$.$ By what percent does this account grow after $1$ quarter?

$2$c$.$ By what percent does this account grow after $1$ year? This is the APY.