A debt of $\$ 5669.51$ is due April 1,2025 . What is the value of the obligation on January 1,2017 , if money is worth $2 \%$ compounded quarterly?
The value of the obligation is $\$$
(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：The problem is asking for the present value of a future debt. The present value formula is used to calculate the present value of a certain amount of money to be received in the future, given a certain interest rate. The formula is: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\) where: \(PV\) is the present value, \(FV\) is the future value, \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 2 ：In this case, \(FV = \$5669.51\), \(r = 2\%\) or \(0.02\), \(n = 4\) (since the interest is compounded quarterly), and \(t = 8\) years (from January 1, 2017 to April 1, 2025).

Step 3 ：Substitute the given values into the formula: \(PV = \frac{5669.51}{(1 + \frac{0.02}{4})^{4*8}}\)

Step 4 ：Solving the equation gives \(PV = 4833.1641944719595\)

Step 5 ：Rounding to the nearest cent gives the final answer: \(\boxed{\$4833.16}\)