john has $4,069 in an account. the interest rate is 12% compounded annually. to the nearest cent, how much…

john has $4,069 in an account. the interest rate is 12% compounded annually. to the nearest cent, how much interest will he earn in 1 year? 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.

john has $4,069 in an account. the interest rate is 12% compounded annually. to the nearest cent, how much interest will he earn in 1 year? 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: Convertir tasa de interés a decimal

Dado que $r = 12%=0.12$, $p = 4069$ y $t = 1$.

Step2: Calcular el saldo final

Usamos la fórmula $B=p(1 + r)^t$. Sustituyendo los valores: $B = 4069\times(1 + 0.12)^1=4069\times1.12 = 4557.28$.

Step3: Calcular el interés ganado

El interés $I$ es $I=B - p$. Entonces $I=4557.28-4069 = 488.28$.

Answer:

$488.28$