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.
After 3 years, he will have $4499.45
steps:
4000*1.04
=4160*1.04
=4326.4*1.04
=4499.456
To calculate the amount in the investment account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial investment (principal)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the initial investment (P) is $4,000. The annual interest rate (r) is 4% or 0.04 as a decimal. Since the interest is compounded annually, the compounding frequency (n) is 1. The time period (t) is 3 years.
Plugging in the values into the formula:
A = 4000(1 + 0.04/1)^(1*3)
A = 4000(1.04)^3
Now, we can calculate the future value of the investment after 3 years using a calculator or by hand.
A = 4000(1.124864)
A ≈ $4,499.46
Rounding to the nearest dollar, the amount in the account after 3 years is $4,499.