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.
The formula to find the final amount of an investment with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (the initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $15,000
r = 3.4% = 0.034
n = 4 (quarterly compounding)
t = 27 years
Plugging in the values into the formula:
A = 15000(1 + 0.034/4)^(4*27)
Calculating inside the parentheses:
A = 15000(1 + 0.0085)^(108)
Calculating the exponent:
A = 15000(1.0085)^(108)
Calculating the final amount (A):
A ≈ $41,013.38
Therefore, the final amount of the investment after 27 years with quarterly compounding is approximately $41,013.38.