Chris invested $15000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27years if interest is compound quarterly. Round to the nearest cent
To find the final amount of the investment after 27 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal (initial investment) = $15000
r = annual interest rate = 3.4% = 0.034 (as a decimal)
n = number of times interest is compounded per year = 4 (quarterly)
t = number of years = 27
Plugging in the values:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying further:
A = 15000(1.0085)^(108)
Using a calculator to find the value of (1.0085)^(108), we get approximately 1.89286919.
A ≈ 15000(1.89286919)
A ≈ 28393.04
Therefore, the final amount of the investment after 27 years if interest is compounded quarterly is approximately $28,393.04.