A bank features a savings account that has an annual percentage rate of $2\mathrm{.}4\%$ with interest compounded quarterly. Caroline deposits $$3,500$ into the account.

How much money will Caroline have in the account in $1$ year?

Answer $=$$ Round answer to the nearest penny.

What is the annual percentage yield $($APY$)$ for the savings account? APY$=\%.$ Round to the nearest hundredth of a percent.