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 of the investment after 27 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, Chris' initial investment (P) is $15,000, the annual interest rate (r) is 3.4% (or 0.034 as a decimal), interest is compounded quarterly (n = 4), and the investment period (t) is 27 years.
Plugging these values into the formula, we get:
A = $15000(1 + 0.034/4)^(4*27)
After evaluating the expression, we find that the final amount of the investment is approximately $39,456.23.