karen has $20 in an account that earns 10% interest compounded annually. to the nearest cent, how much will…

karen has $20 in an account that earns 10% interest compounded annually. to the nearest cent, how much will she 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.

karen has $20 in an account that earns 10% interest compounded annually. to the nearest cent, how much will she 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

Explanation:

Step1: Identify values

$p = 20$, $r=0.1$, $t = 2$

Step2: Substitute into formula

$B=20\times(1 + 0.1)^{2}$

Step3: Calculate exponent

$(1 + 0.1)^{2}=1.1^{2}=1.21$

Step4: Calculate final amount

$B=20\times1.21 = 24.2$

Answer:

$24.20$