felix has $5,483 in an account. the interest rate is 12% compounded annually. to the nearest cent, how much…

felix has $5,483 in an account. the interest rate is 12% 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.

felix has $5,483 in an account. the interest rate is 12% 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: Convert interest rate to decimal

$r = 12%=0.12$

Step2: Identify principal and time

$p = 5483$, $t = 2$

Step3: Calculate the balance

$B=p(1 + r)^t=5483\times(1 + 0.12)^2=5483\times1.12^2=5483\times1.2544$ $B = 6888.9752$

Step4: Calculate the interest

$I=B - p=6888.9752-5483 = 1405.9752\approx1405.98$

Answer:

$1405.98$