Pay Dirt Photo illustration by Slate. Photos by Getty Images Plus. Pay Dirt is Slate’s money advice column. Have a question? Send it to Kristin and Ilyce here . (It’s anonymous!) Dear Pay Dirt, My question involves splitting investment in a house after a break up. I purchased a house on a 30-year-mortgage at 4.5 percent interest. After two years, my (then) partner moved in, and we evened up on the equity and agreed to split the mortgage payments moving forward. He suggested refinancing when he moved in (15-year-mortgage at a 3 percent interest rate) which saved $55,000 over course of the loan. We paid together toward the house for two years, and then he lost his job and I took over the mortgage payments (and utilities and repair/maintenance costs) for the next 10 years. We recently broke up. How do I fairly compensate him for his investment in the house? He claims that, since refinancing was his idea, he can count the $55,000 we saved in interest as a contribution to the house.…