Consider a shared$-$appreciation mortgage $($SAM$)$ on a $$250,000$ mortgage with yearly payments. Current market mortgage rates are high, running at $13\%,$ of which $10\%$ is annual inflation. Under the terms of the SAM, a $15-$ year mortgage is offered at $5\%.$ After $15$ years, the house must be sold, and the bank retains $$400,000$ of the sale price. If inflation remains at $10\%,$ what are the cash flows to the bank? To the owner?