noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much…

noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much interest will he earn 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.

noah deposited $4,096 in an account earning 14% interest compounded annually. to the nearest cent, how much interest will he earn 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

$p = 4096$, $r=0.14$, $t = 4$

Step2: Calculate the balance $B$

$B=p(1 + r)^t=4096\times(1 + 0.14)^4$ First, calculate $(1 + 0.14)^4=(1.14)^4=1.14\times1.14\times1.14\times1.14 = 1.68896016$. Then, $B = 4096\times1.68896016=6918.9707$.

Step3: Calculate the interest

Interest $=B - p$. Interest $=6918.9707-4096 = 2822.9707\approx2822.97$

Answer:

$2822.97$