Nope that will not work. You need to be at 80% of the appraised value. Sale price has nothing to do with it at all.
When I bought in 1998 with 5% down, I only had a reappraisal done in three years. The housing market was rising, and though I had only paid another $1500 to the principleprincipal, the house appraised for $25,000 more than when I bought it so it was no problem getting rid of it.