lara has $8,770 in an account that earns 9% interest compounded annually. to the nearest cent, how much…

lara has $8,770 in an account that earns 9% interest compounded annually. to the nearest cent, how much interest will she 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.

lara has $8,770 in an account that earns 9% interest compounded annually. to the nearest cent, how much interest will she 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 the values

$p = 8770$, $r=0.09$, $t = 4$

Step2: Calculate the balance $B$

$B=p(1 + r)^t=8770\times(1 + 0.09)^4$ First, calculate $(1 + 0.09)^4=1.09^4=1.09\times1.09\times1.09\times1.09 = 1.41158161$. Then, $B = 8770\times1.41158161\approx12379.56062$.

Step3: Calculate the interest

Interest $=B - p$. Interest $=12379.56062-8770=3609.56062\approx3609.56$.

Answer:

$3609.56$