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 calculate the future value of an investment with compound interest is:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (the initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Given:
P = $15,000
r = 3.4% = 0.034 (expressed as a decimal)
n = 4 (compounded quarterly)
t = 27 years
Applying the values to the formula:
A = 15000(1 + 0.034/4)^(4*27)
Calculating inside the parentheses:
A = 15000(1 + 0.0085)^(4*27)
A = 15000(1.0085)^(108)
Calculating the exponent:
A ≈ 15000(2.432481584)
Calculating the product:
A ≈ $36,487.22
Therefore, the final amount of the investment after 27 years would be approximately $36,487.22.