Chris invest $15,000 in a retirement account with an annual 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 for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Given:
P = $15,000
r = 3.4% or 0.034
n = 4 (quarterly)
t = 27 years
Plugging in the values into the formula, we have:
A = 15000(1 + 0.034/4)^(4*27)
Calculating inside the parentheses first:
A = 15000(1 + 0.0085)^(4*27)
A = 15000(1.0085)^108
Calculating 1.0085^108:
A = 15000 * 3.14391969
Calculating the final amount:
A = $47,158.80
Rounded to the nearest cent, the final amount of the investment after 27 years would be $47,158.80.