13. $22. The last day Smith took $6 from the purse. It means that from there was $12 before he took half of the existing money. Since every time, before taking money, he added $5, then there was $12-$5=$7 in the wallet after the second day. Since he took half of the existing money and there was left $7 second day, then there was 2x$7=$14 on the second day, before he added $5. So after the first day, there was $14-$5=$9 in the wallet. Doing the same for the first day we see that there was 2x$9=$18 before he took his portion. So, Smith took altogether, $9+$7+$6=$22 as a salary.