Question

sidney has $8,684 in an account that earns 10% interest compounded annually. to the nearest cent, how much will she have in 4 years? use the formula $b = p(1 + r)^t$, where $b$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years.

Explanation:

Step1: Identify given values

$p = 8684$, $r = 0.10$, $t = 4$

Step2: Substitute into compound interest formula

$B = 8684(1 + 0.10)^4$

Step3: Calculate the growth factor

$(1.10)^4 = 1.4641$

Step4: Compute the final balance

$B = 8684 \times 1.4641$
$B = 12714.2444$

Step5: Round to nearest cent

$B = 12714.24$

Answer:

$\$12714.24$