eric has $5,647 in an account. the interest rate is 4% compounded annually. to the nearest cent, how much…

eric has $5,647 in an account. the interest rate is 4% compounded annually. to the nearest cent, how much interest will he 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.

eric has $5,647 in an account. the interest rate is 4% compounded annually. to the nearest cent, how much interest will he 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: Identify the values

$p = 5647$, $r=0.04$, $t = 2$

Step2: Calculate the final balance $B$

$B=p(1 + r)^t=5647\times(1 + 0.04)^2=5647\times1.04^2=5647\times1.0816=6107.5952$

Step3: Calculate the interest earned

Interest $=B - p=6107.5952-5647 = 460.5952\approx460.60$

Answer:

$460.60$