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 $A _ { N } = 3,000 ( 1 + 0.04 ) ^ { N }$ , $N = 1,2,3 , \ldots$ 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) $A _ { 20 } = \$ 6,321$

Question

Quizplus · Accepted Answer

Using the formula $A_N = P(1+r)^N$, where $P$ is the principal deposit, $r$ is the interest rate as a decimal, and $N$ is the number of years:

$A_{20} = 3000(1+0.04)^{20} \approx 6573.15$

Rounding to the nearest cent, the answer is $\boxed{	extbf{(C) } A_{20} = \$6,573}$.

A Deposit Of $3,000\$ 3,000$3,000 Is Made in an Account That Earns

A Deposit Of $\$ 3,000$ Is Made in an Account That Earns