sidney has $8,684 in an account that earns 10% interest compounded annually. to the nearest cent, how much…

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.

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.

Answer

Explanation:

Step1: Identify values

$p = 8684$, $r=0.1$, $t = 4$

Step2: Substitute into formula

$B = 8684\times(1 + 0.1)^{4}$

Step3: Calculate exponent

$(1 + 0.1)^{4}=1.1^{4}=1.4641$

Step4: Calculate final amount

$B = 8684\times1.4641=\ 12714.2444$

Answer:

$12714.24$