Question

an investment of $400 grows at a 7% interest rate, compounded annually. what is the value of the investment after 3 years?
annual compound interest formula
a = p(1 + r)^t
a = $?

Explanation:

Step1: Identify given values

Here, \( P = 400 \) (principal amount), \( r = 7\% = 0.07 \) (annual interest rate), \( t = 3 \) (number of years).

Step2: Apply compound interest formula

The formula for annual compound interest is \( A = P(1 + r)^t \). Substitute the values:
\( A = 400(1 + 0.07)^3 \)

Step3: Calculate \( (1 + 0.07)^3 \)

First, \( 1 + 0.07 = 1.07 \). Then, \( 1.07^3 = 1.07\times1.07\times1.07 = 1.225043 \)

Step4: Calculate \( A \)

Multiply by the principal: \( A = 400\times1.225043 = 490.0172 \)

Answer:

\( 490.02 \) (rounded to the nearest cent)