suzie has $9,126 in an account. the interest rate is 10% compounded annually. to the nearest cent, how much…

suzie has $9,126 in an account. the interest rate is 10% compounded annually. to the nearest cent, how much interest will she earn in 5 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.

suzie has $9,126 in an account. the interest rate is 10% compounded annually. to the nearest cent, how much interest will she earn in 5 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

$p = 9126$, $r=0.1$, $t = 5$

Step2: Calculate the final amount $B$

$B=p(1 + r)^t=9126\times(1 + 0.1)^5=9126\times1.1^5$ $1.1^5=1.1\times1.1\times1.1\times1.1\times1.1 = 1.61051$ $B=9126\times1.61051=14697.51326$

Step3: Calculate the interest

Interest $=B - p=14697.51326-9126 = 5571.51326\approx5571.51$

Answer:

$5571.51$