Question

maggie has $2,674 in an account that earns 5% interest compounded annually. to the nearest cent, how much interest will she earn 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.

Explanation:

Step1: Identify values

Principal \( p = 2674 \), rate \( r = 0.05 \), time \( t = 2 \).

Step2: Calculate balance \( B \)

Using formula \( B = p(1 + r)^t \), substitute values:
\( B = 2674(1 + 0.05)^2 = 2674(1.05)^2 \).
First, \( 1.05^2 = 1.1025 \). Then, \( 2674 \times 1.1025 = 2949.085 \).

Step3: Find interest earned

Interest = \( B - p = 2949.085 - 2674 = 275.085 \), round to nearest cent: \( 275.09 \).

Answer:

\( 275.09 \)