Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the total amount of the investment after 27 years if interest is compounded quarterly.
Round the answer to the nearest cent
The final amount of the investment after 27 years is $______.
To find the total amount of the investment after 27 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the initial investment amount ($15,000)
r = the annual interest rate (3.4% or 0.034 as a decimal)
n = the number of times interest is compounded per year (quarterly, so 4 times)
t = the number of years (27)
Plugging in the given values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying this expression, we get:
A = 15000(1.0085)^(108)
Using a calculator, we find:
A ≈ $32,404.57
Rounding to the nearest cent, the final amount of the investment after 27 years is $32,404.57. Answer: \boxed{32404.57}.