A deposit of $\$3,000$ is made in an account that earns $4\%$ interest compounded yearly. The balance in the account after N years is given by $A_N=3,000(1+0.04{)}^N$ , $N=1,2,3,\dots$ Find the balance in this account after $20$ years by computing $A_{20}$ . Round your answer to the nearest cent.

A) $A_{20}=\$5,403$
B) $A_{20}=\$62,400$
C) $A_{20}=\$6,573$
D) $A_{20}=\$3,245$
E) $A_{20}=\$6,321$

Compounded Yearly

Calculating interest on an investment or loan annually, where the accrued interest is added to the principal sum each year.

Interest Rate

The proportion of a loan charged as interest to the borrower, typically expressed as an annual percentage of the outstanding loan.

Balance

A condition in which different elements are equal or in the correct proportions, often used in financial contexts to denote the amount of money available in an account.