Question

nate deposited $1,000 in an account earning 5% interest compounded annually. to the nearest cent, how much will he have in 4 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

\( p = 1000 \), \( r = 0.05 \) (5% as decimal), \( t = 4 \)

Step2: Apply formula

\( B = 1000(1 + 0.05)^4 \)
Calculate \( (1.05)^4 \approx 1.21550625 \)
Multiply by \( p \): \( B = 1000 \times 1.21550625 = 1215.50625 \)

Step3: Round to cent

\( 1215.50625 \approx 1215.51 \)

Answer:

\( \$1215.51 \)