Question

use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually
$11,000 invested at an apr of 2.3% for 19 years.

the balance in the account after 19 years is $\square
(round to the nearest cent as needed )

Explanation:

Step1: Recall compound interest formula

The compound interest formula for annual compounding is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years.
Here, $P = 11000$, $r = 0.023$ (since $2.3\%= \frac{2.3}{100}=0.023$), and $t = 19$.

Step2: Substitute values into formula

Substitute $P = 11000$, $r = 0.023$, and $t = 19$ into the formula:
$A = 11000(1 + 0.023)^{19}$

Step3: Calculate $(1 + 0.023)^{19}$

First, calculate $1 + 0.023 = 1.023$. Then, find $1.023^{19}$. Using a calculator, $1.023^{19}\approx1.530847$.

Step4: Calculate final amount $A$

Multiply $11000$ by $1.530847$:
$A = 11000\times1.530847\approx16839.32$

Answer:

$\$16839.32$