Question

suzie has $9,126 in an account. the interest rate is 10% compounded annually. to the nearest cent, how much interest will she earn in 5 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 \( p = 9126 \), rate \( r = 0.10 \), time \( t = 5 \).

Step2: Calculate balance \( B \)

Using \( B = p(1 + r)^t \), substitute values:
\( B = 9126(1 + 0.10)^5 = 9126(1.1)^5 \).
Calculate \( 1.1^5 = 1.61051 \), so \( B = 9126 \times 1.61051 \approx 14697.51 \).

Step3: Find interest earned

Interest = \( B - p = 14697.51 - 9126 = 5571.51 \).

Answer:

\( 5571.51 \)