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 compounded quarterly is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or the loan is made for.
In this case, P = $15,000, r = 3.4%, n = 4 (compounded quarterly), and t = 27 years.
A = $15,000(1 + 0.034/4)^(4 * 27)
Using a calculator, the final amount is approximately $37,131.91.