An author is to be paid royalties for publishing a book. Two alternative offers are made:

$($a$)$ The author can be paid $$20825$ immediately,

$($b$)$ There can be $7$ equal annual payments of $$3562,$ the first being paid at once.

Calculate the difference between the present values of the two offers by subtracting the present value of option $($b$)$ from the present value of option $($a$).$

Assume the interest rate is $6\%$ per annum. Report your answer to the nearest cent with an appropriate sign.