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 answer

The formula to find the final amount of an investment with compound interest is:

A = P(1 + r/n)^(nt)

Where:
A = the final amount of the investment
P = the principal amount (the initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years

In this case:
P = $15,000
r = 3.4% = 0.034
n = 4 (quarterly compounding)
t = 27 years

Plugging in the values into the formula:

A = 15000(1 + 0.034/4)^(4*27)

Calculating inside the parentheses:

A = 15000(1 + 0.0085)^(108)

Calculating the exponent:

A = 15000(1.0085)^(108)

Calculating the final amount (A):

A ≈ $41,013.38

Therefore, the final amount of the investment after 27 years with quarterly compounding is approximately $41,013.38.