2014 AMC 12A Problem 15

A five-digit palindrome is a positive integer with respective digits abcba, where a is non-zero. Let S be the sum of all five-digit palindromes. What is the sum of the digits of S?

\textbf{(A) }9\qquad \textbf{(B) }18\qquad \textbf{(C) }27\qquad \textbf{(D) }36\qquad \textbf{(E) }45\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.