Question

ayana has $730 in an account. the interest rate is 3% compounded annually. to the nearest cent, how much interest will she earn 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

$p = 730$, $r = 0.03$, $t = 3$

Step2: Calculate balance \( B \)

Use formula \( B = p(1 + r)^t \)
\( B = 730(1 + 0.03)^3 \)
\( B = 730(1.03)^3 \)
\( 1.03^3 = 1.092727 \)
\( B = 730 \times 1.092727 \approx 797.69 \)

Step3: Calculate interest

Interest = \( B - p \)
Interest = \( 797.69 - 730 = 67.69 \)

Answer:

\( 67.69 \)