This isn't right. Over time Person #1 should have more savings. Loan interest rates are very low, person #1 shouldn't be putting the money into a savings account, he should be using a better investment. Person #2 is now forgoing the higher return of stocks to pay off the mortgage.

It gets worse for person #2. The house is probably changing in value. If the house goes up in value person #1 is ahead because that money is all his, on the $10k investment, person #2 has a much larger investment to get the same return. If the house goes down person #1 has at most $10k to lose, while person #2 can lose the entire value he has paid in so far.

Of course eventually person #2 has the house paid off and has $2000 to work with.