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 calculate the future value of an investment with compound interest is:

A = P(1 + r/n)^(n*t)

Where:
A = the future value of the investment
P = the principal amount (the initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

Given:
P = $15,000
r = 3.4% = 0.034 (expressed as a decimal)
n = 4 (compounded quarterly)
t = 27 years

Applying the values to the formula:

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

Calculating inside the parentheses:

A = 15000(1 + 0.0085)^(4*27)
A = 15000(1.0085)^(108)

Calculating the exponent:

A ≈ 15000(2.432481584)

Calculating the product:

A ≈ $36,487.22

Therefore, the final amount of the investment after 27 years would be approximately $36,487.22.