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 final amount of the investment after 27 years is
The formula to calculate the final amount of an investment with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (the initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the given values:
P = $15,000
r = 3.4% = 0.034 (as a decimal)
n = 4 (quarterly compounding)
t = 27
A = 15000(1 + 0.034/4)^(4*27)
A ≈ $38,632.45
Therefore, the final amount of the investment after 27 years is approximately $38,632.45.