Question

a savings account starts with $1,000 and earns 4% interest, compounded annually. what is the balance after 3 years?
annual compound interest formula
a = p(1 + r)^t
a = $?
round your answer to the nearest hundredth

Explanation:

Step1: Identify the values

Here, the principal amount \( P = 1000 \), the annual interest rate \( r = 4\%=0.04 \), and the time \( t = 3 \) years.

Step2: Apply the compound interest formula

The formula for annual compound interest is \( A = P(1 + r)^{t} \). Substitute the values:
\( A=1000\times(1 + 0.04)^{3} \)

Step3: Calculate the exponent part

First, calculate \( (1 + 0.04)^{3}=(1.04)^{3} \). \( 1.04\times1.04 = 1.0816 \), then \( 1.0816\times1.04=1.124864 \)

Step4: Calculate the final amount

Multiply by the principal: \( A = 1000\times1.124864 = 1124.864 \)

Step5: Round to the nearest hundredth

Rounding \( 1124.864 \) to the nearest hundredth gives \( 1124.86 \)

Answer:

\( 1124.86 \)