nicholas has $5,495 in an account that earns 14% interest compounded annually. to the nearest cent, how much…

nicholas has $5,495 in an account that earns 14% interest compounded annually. to the nearest cent, how much will he have 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.

nicholas has $5,495 in an account that earns 14% interest compounded annually. to the nearest cent, how much will he have 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: Identify values

$p = 5495$, $r=0.14$, $t = 4$

Step2: Substitute into formula

$B=5495\times(1 + 0.14)^{4}$

Step3: Calculate inside parentheses

$1+0.14 = 1.14$

Step4: Calculate exponent

$1.14^{4}=1.14\times1.14\times1.14\times1.14=1.68896016$

Step5: Multiply by principal

$B = 5495\times1.68896016\approx9270.84$

Answer:

$9270.84$