An investment account earns 4% per year compounded annually. If the initial investment was $4,000.00, how much is in the account after 3 years? Round your answer to the nearest dollar.
To calculate the amount in the account after 3 years, we multiply the initial investment by the growth factor. The growth factor is calculated by adding 1 to the interest rate (expressed as a decimal), and then raising it to the power of the number of years.
The interest rate is 4% per year, so it can be expressed as 0.04 (since 4% is equivalent to 0.04 as a decimal).
The growth factor is therefore (1 + 0.04)^3.
Calculating that expression:
(1 + 0.04)^3 = 1.04^3 = 1.124864
Now, we multiply the initial investment by the growth factor:
$4,000.00 * 1.124864 = $4,499.46
Rounding to the nearest dollar, the amount in the account after 3 years is $4,499.