Question

polly deposited $3,634 in an account earning 5% interest compounded annually. to the nearest cent, how much will she have in 3 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.

Explanation:

Step1: Identify values

$p = 3634$, $r = 0.05$, $t = 3$

Step2: Apply formula

$B = p(1 + r)^t = 3634(1 + 0.05)^3$

Step3: Calculate $(1.05)^3$

$(1.05)^3 = 1.05×1.05×1.05 = 1.157625$

Step4: Multiply by principal

$B = 3634×1.157625 = 4207.81925$

Step5: Round to cent

$4207.82$

Answer:

$\$4207.82$