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 $
.
To find the final amount of the investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (in this case, $15,000)
r = the annual interest rate (3.4% expressed as 0.034)
n = the number of times the interest is compounded per year (quarterly = 4)
t = the number of years (27)
Plugging in the given values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying the expression inside the parentheses:
A = 15000(1 + 0.0085)^(108)
Calculating the exponent:
A = 15000(1.0085)^108
Calculating (1.0085)^108:
A ≈ 15000 * 2.4034
A ≈ 36051
The final amount of the investment after 27 years is approximately $36,051.