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 for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal amount is $15,000, the annual interest rate is 3.4% (or 0.034 as a decimal), the interest is compounded quarterly (so n = 4), and the investment is held for 27 years (so t = 27).
Plugging in these values into the formula:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying:
A = 15000(1.0085)^(108)
Calculating:
A ≈ 15000(3.172072)
A ≈ $47,581.08
Therefore, the final amount of the investment after 27 years, compounded quarterly, is $47,581.08.