The problem asks to find the future value of an ordinary annuity. The annuity involves payments of $3,000 made quarterly for 4 years, with an interest rate of 6% compounded quarterly. We need to round the answer to the nearest cent.

1. Problem Description

The problem asks to find the future value of an ordinary annuity. The annuity involves payments of $3,000 made quarterly for 4 years, with an interest rate of 6% compounded quarterly. We need to round the answer to the nearest cent.

2. Solution Steps

The formula for the future value of an ordinary annuity is:

$FV = P * \frac{(1 + r)^n - 1}{r}$

Where:

$FV$ is the future value of the annuity

$P$ is the periodic payment

$r$ is the interest rate per period

$n$ is the number of periods

First, we need to determine the values of $P$, $r$, and $n$.

$P = 3000$ (quarterly payment)

The annual interest rate is 6%, so the quarterly interest rate is:

$r = \frac{0.06}{4} = 0.015$

The annuity is for 4 years, and payments are made quarterly, so the number of periods is:

$n = 4 \times 4 = 16$

Now, we can plug these values into the formula:

$FV = 3000 * \frac{(1 + 0.015)^{16} - 1}{0.015}$

$FV = 3000 * \frac{(1.015)^{16} - 1}{0.015}$

$FV = 3000 * \frac{1.2689855 - 1}{0.015}$

$FV = 3000 * \frac{0.2689855}{0.015}$

$FV = 3000 * 17.9323666$

$FV = 53797.10$

3. Final Answer

$53797.10