albert has $1,000 in an account. the interest rate is 5% compounded annually. to the nearest cent, how much…

albert has $1,000 in an account. the interest rate is 5% 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.

albert has $1,000 in an account. the interest rate is 5% 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

Answer:

$215.51$

Explanation:

Step1: Identify values

$p = 1000$, $r=0.05$, $t = 4$

Step2: Calculate final balance

$B=p(1 + r)^{t}=1000\times(1 + 0.05)^{4}=1000\times1.05^{4}$ $1.05^{4}=1.05\times1.05\times1.05\times1.05 = 1.21550625$ $B = 1000\times1.21550625=1215.50625$

Step3: Calculate interest

Interest $=B - p=1215.50625-1000 = 215.50625\approx215.51$