hugo has $192 in an account. the interest rate is 12% compounded annually. to the nearest cent, how much…

hugo has $192 in an account. the interest rate is 12% 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.

hugo has $192 in an account. the interest rate is 12% 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: Convert interest rate to decimal

$r = 12%=0.12$

Step2: Identify principal and time

$p = 192$, $t = 4$

Step3: Calculate the balance

$B=p(1 + r)^t=192\times(1 + 0.12)^4$ $B=192\times1.12^4$ $1.12^4=1.12\times1.12\times1.12\times1.12 = 1.57351936$ $B=192\times1.57351936=302.11571712$

Step4: Calculate the interest

$I=B - p$ $I=302.11571712-192 = 110.11571712\approx110.12$

Answer:

$110.12$