Langara Woodcraft borrowed money to purchase equipment. The loan is repaid by making payments of $969.94 at the end of every three months over five years. If interest is 6.8% compounded annually, what was the original loan balance?
The original loan balance was $
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：This problem involves calculating the present value of an annuity due. The formula for the present value of an annuity due is: \(PV = PMT \times \left[(1 - (1 + r/n)^{nt}) / (r/n)\right] \times (1 + r/n)\), where:

Step 2 ：\(PV\) is the present value (the original loan balance we're trying to find)

Step 3 ：\(PMT\) is the payment amount per period ($969.94)

Step 4 ：\(r\) is the annual interest rate (6.8% or 0.068)

Step 5 ：\(n\) is the number of compounding periods per year (4, since payments are made quarterly)

Step 6 ：\(t\) is the number of years (5)

Step 7 ：We can plug in the given values into this formula to find the original loan balance.

Step 8 ：Let's calculate: \(PMT = 969.94\), \(r = 0.068\), \(n = 4\), \(t = 5\)

Step 9 ：Substitute these values into the formula, we get \(PV = 16606.402574753323\)

Step 10 ：Rounding to the nearest cent, the original loan balance was \(\boxed{16606.40}\)