tara has $3,906 in an account that earns 12% interest compounded annually. to the nearest cent, how much…

tara has $3,906 in an account that earns 12% interest 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.

tara has $3,906 in an account that earns 12% interest 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 the values

$p = 3906$, $r=0.12$, $t = 5$

Step2: Calculate the final amount $B$

$B=p(1 + r)^t=3906\times(1 + 0.12)^5$ $B=3906\times(1.12)^5$ $(1.12)^5=1.12\times1.12\times1.12\times1.12\times1.12 = 1.7623416832$ $B=3906\times1.7623416832\approx6883.60$

Step3: Calculate the interest

Interest $=B - p$ Interest $=6883.60-3906 = 2977.60$

Answer:

$2977.60$