\#15. (24 points) Use the following short rate tree. Short rate can increase or decrease in 6 months by equal probability. Use semi-annual compounding. Now, consider a 1 year mortgage (semi-annually paid) with a mortgage rate of 8% (so that a semiannual mortgage rate is 4% ) and an initial principal balance of $20,000. The mortgage is divided into three sequential pay tranches. Tranche A receives the first $6,000 of the principal, tranche B receives the next $6,000 of the principal, and tranche C receives the remaining $8,000 of the principal. (a) ( 3 points) Fill in the amortization schedule of the whole mortgage below