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# 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.

1. Fill in the amortization schedule of the whole mortgage below.

2. Fill the scheduled payments to the A, B, and C tranches, assuming no prepayment.

3. Suppose that exactly 30% 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.

4. Compute the present value of the whole mortgage, tranche A, tranche B, and tranche C, respectively.

5. Briefly explain the difference between value-minimizing prepayment policy and deterministic prepayment policy and how you would value the mortgage under value-minimizing prepayment policy.

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