The problem asks to find the future value of an ordinary annuity of $3,000 paid quarterly for 4 years, given an interest rate of 6% compounded quarterly. The answer should be rounded to the nearest cent.

1. Problem Description

The problem asks to find the future value of an ordinary annuity of $3,000 paid quarterly for 4 years, given an interest rate of 6% compounded quarterly. The answer should be rounded to the nearest cent.

2. Solution Steps

First, we need to determine the inputs for the future value of an ordinary annuity formula.

Payment (PMT) = $3,000

Interest rate per period (i) = Annual interest rate / Number of compounding periods per year = 6% / 4 = 0.06 / 4 = 0.015

Number of periods (n) = Number of years * Number of compounding periods per year = 4 * 4 = 16

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

$FV = PMT * \frac{(1+i)^n - 1}{i}$

Plugging in the values:

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

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

$FV = 3000 * \frac{1.268985548 - 1}{0.015}$

$FV = 3000 * \frac{0.268985548}{0.015}$

$FV = 3000 * 17.93236987$

$FV = 53797.10961$

Rounding to the nearest cent, we get $53797.

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3. Final Answer

$53797.11