Question

emmett deposited $90 in an account earning 5% interest compounded annually.
to the nearest cent, how much will he 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.
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Explanation:

Step1: Identify values for p, r, t

p = 90, r = 0.05 (5% as decimal), t = 2

Step2: Substitute into formula \( B = p(1 + r)^t \)

\( B = 90(1 + 0.05)^2 \)

Step3: Calculate \( (1 + 0.05)^2 \)

\( (1.05)^2 = 1.1025 \)

Step4: Multiply by p

\( B = 90 \times 1.1025 = 99.225 \)

Step5: Round to nearest cent

99.23 (since 0.225 rounds up to 0.23 when to nearest cent)

Answer:

\$99.23