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
To find the final amount after 27 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
Given:
P = $15,000
r = 3.4% = 0.034 (annual interest rate in decimal form)
n = 4 (quarterly compounding)
t = 27 years
Substituting these values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Calculating this expression, we find:
A ≈ $32,417.22
Rounding this value to the nearest cent, the final amount of the investment after 27 years is $32,417.22.