Here is my Java 7 solution:

    // To count a's in string s
    int aCount = 0;
    // To count a's in infinite string
    long Totalcount = 0;

    // Counting a's in string s
    for (int i=0; i<s.length(); i++) {
        char letter = s.charAt(i);
        if (letter == 'a') { aCount++; }
    }

    // Counting a's in infinite string

    // Check whether n is a multiple of s.length()
    if (n % s.length() == 0) {
        Totalcount = (n / s.length()) * aCount;
    } 
    else {
        // Calculate the nearest multiple of s.length() to n
        long nearestMultiple = n - (n%s.length());
        // Add a's count up to nearest multiple
        Totalcount = (nearestMultiple / s.length()) * aCount;

        // Add the remaining a's count in the remaining string
        for (int i=0; i<n%s.length(); i++) {
            char letter = s.charAt(i);
            if (letter == 'a') { Totalcount++; }
        }
    }

    return Totalcount;