2002 AMC 12A Problem 21

Consider the sequence of numbers: 4,7,1,8,9,7,6,\ldots For n>2, the n-th term of the sequence is the units digit of the sum of the two previous terms. Let S_n denote the sum of the first n terms of this sequence. The smallest value of n for which S_n>10,000 is:

\text{(A) }1992 \qquad \text{(B) }1999 \qquad \text{(C) }2001 \qquad \text{(D) }2002 \qquad \text{(E) }2004

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