Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly.
Round the answer to the nearest cent.(1 point)
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $15,000
r = 3.4% or 0.034
n = 4 (quarterly compounding)
t = 27 years
Substituting the values into the formula, we have:
A = 15000(1 + 0.034/4)^(4*27)
A ≈ 15000(1 + 0.0085)^(108)
A ≈ 15000(1.0085)^108
A ≈ 15000(2.208756602)
A ≈ $33,131.35
Therefore, the final amount of the investment after 27 years with quarterly compounding is approximately $33,131.35.