Use the following short rate tree. Short rate can increase or decrease in 6 months by equal probability. Use semi-annual compounding.

Time 0 Time 0.5 12%

10%

8%

Now, consider a 1 year mortgage (semi-annually paid) with a semi-annual mortgage rate of 10% and initial principal balance of $10,000. The mortgage is divided into three sequential pay tranches. Tranche A receives the first $3,000 of principal, tranche B receives the next $3,000 of principal, and tranche C receives the remaining $4,000 of principal. there are 6 sub questions. please show the intermediate steps in details. thx so much!

pls someone help me to deal with this question! it is an urgent event!!!

\#3. 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 semi-annual mortgage rate of 10% and initial principal balance of $10,000. The mortgage is divided into three sequential pay tranches. Tranche A receives the first $3,000 of principal, tranche B receives the next $3,000 of principal, and tranche C receives the remaining $4,000 of principal. (a) Fill in the amortization schedule of the whole mortgage below. (b) Fill the scheduled payments to the A, B, and C tranches, assuming no prepayment. (c) According to the interest tree, calculate 6-month discount factor for each node. Moreover, compute 1-year discount factor today. (d) Assuming that there are no prepayments, what is the value of (i) the whole mortgage? (ii) tranche A ? (iii) tranche B ? (iv) tranche C? e) Suppose the mortgagor can pay off the mortgage on any payment date by paying the remaining principal balance. Assuming the mortgagor follows yalue-minimixing prepayment policy. Determine the value of the whole mortgage, tranche A, tranche B, and tranche C, respectively. (f) Suppose that exactly 50% of mortgages will prepay in full after 6 months ( 0.5 year), regardless of the level of interest rates. Fill the amortization schedule based on the deterministic prepayment. Moreover, compute the present value of the whole mortgage, tranche A, tranche B, and tranche C, respectively