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 10% (so that a semi-annual mortgage rate is 5% ) and an initial principal balance of $20,000. The mortgage is divided into three sequential pay tranches. Tranche A receives the first $8,000 of the principal, tranche B receives the next $6,000 of the principal, and tranche C receives the remaining $6,000 of the principal. 4. Compute the present value of the whole mortgage, tranche A, tranche B, and tranche C, respectively. 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 10% (so that a semi-annual mortgage rate is 5% ) and an initial principal balance of $20,000. The mortgage is divided into three sequential pay tranches. Tranche A receives the first $8,000 of the principal, tranche B receives the next $6,000 of the principal, and tranche C receives the remaining $6,000 of the principal. 4. Compute the present value of the whole mortgage, tranche A, tranche B, and tranche C, respectively