brendan deposited $3,967 in an account earning 5% interest compounded annually. to the nearest cent, how…

brendan deposited $3,967 in an account earning 5% interest compounded annually. to the nearest cent, how much interest will he 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.

brendan deposited $3,967 in an account earning 5% interest compounded annually. to the nearest cent, how much interest will he 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 the values

$p = 3967$, $r=0.05$, $t = 5$

Step2: Calculate the final amount $B$

$B=p(1 + r)^t=3967\times(1 + 0.05)^5=3967\times1.05^5$ $1.05^5=1.05\times1.05\times1.05\times1.05\times1.05 = 1.27628$ $B=3967\times1.27628\approx5063.00$

Step3: Calculate the interest

Interest $=B - p=5063.00-3967 = 1096.00$

Answer:

$1096.00$