Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. 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. (2 points)
To calculate the amount in the account after 3 years with 4% annual interest compounded annually, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = annual interest rate as a decimal
n = number of times that interest is compounded per year
t = number of years the money is invested for
In this case:
P = $4,000.00
r = 4% = 0.04
n = 1 (compounded annually)
t = 3 years
Plugging in the values:
A = $4,000.00(1 + 0.04/1)^(1*3)
A = $4,000.00(1 + 0.04)^3
A = $4,000.00(1.04)^3
A = $4,000.00(1.124864)
A = $4,499.46
Therefore, the amount in the account after 3 years would be approximately $4,499.46.