andy has $1,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much…

andy has $1,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much will he have 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.

andy has $1,000 in an account. the interest rate is 15% compounded annually. to the nearest cent, how much will he have 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

Answer:

$1322.50$

Explanation:

Step1: Convert interest rate to decimal

$r = 15%=0.15$

Step2: Identify principal and time

$p = 1000$, $t = 2$

Step3: Substitute values into formula

$B=p(1 + r)^{t}=1000\times(1 + 0.15)^{2}$

Step4: Calculate the value inside parentheses

$1+0.15 = 1.15$

Step5: Calculate the exponent

$(1.15)^{2}=1.15\times1.15 = 1.3225$

Step6: Calculate the final amount

$B = 1000\times1.3225=1322.50$