Question

use the compound interest formula to determine the accumulated balance after the stated period
$6000 invested at an apr of 5% for 4 years

if interest is compounded annually, what is the amount of money after 4 years?
$
(do not round until the final answer. then round to the nearest cent as needed.)

Explanation:

Step1: Recall compound interest formula

The compound interest formula when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years.
Here, $P = 6000$, $r = 0.05$ (since 5% = 0.05), and $t = 4$.

Step2: Substitute values into formula

Substitute $P = 6000$, $r = 0.05$, and $t = 4$ into the formula:
$A = 6000(1 + 0.05)^4$

Step3: Calculate the exponent

First, calculate $(1 + 0.05)^4=(1.05)^4$.
$1.05^4 = 1.05\times1.05\times1.05\times1.05 = 1.21550625$

Step4: Multiply by principal

Now, multiply by $P = 6000$:
$A = 6000\times1.21550625 = 7293.0375$

Step5: Round to nearest cent

Rounding $7293.0375$ to the nearest cent (two decimal places) gives $7293.04$.

Answer:

$7293.04$