debbie has $4,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much…

debbie has $4,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much interest will she earn in 2 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.

debbie has $4,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much interest will she earn in 2 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: Convert interest rate to decimal

$r = 15%=0.15$

Step2: Identify principal and time

$p = 4000$, $t = 2$

Step3: Calculate the final balance

$B=p(1 + r)^t=4000\times(1 + 0.15)^2=4000\times1.15^2=4000\times1.3225 = 5290$

Step4: Calculate the interest earned

Interest $=B - p=5290-4000 = 1290$

Answer:

$1290.00$