Consider a binomial tree for interest rates as discussed in class. The interest rate the first period is 4% and rates move up or down by 1% per year; all interest rates are compounded annually. The probability of a move up is 60% (different assumption than in class). All calculations should be done using the full precision of your calculator and computer. It is strongly suggested that you use Excel to make this easier. Answers which are an interest rate or a yield should be expressed with two decimal places showing basis points. Answers which are dollar amounts should include two decimals showing cents, Use the tree to determine the value of 3-year zero coupon bond with face value of $100 incorporating the interest rate uncertainty. Repeat the calculation for a 2-year zero and for a 1-year zero. Use the valuations from the prior questions to determine the spot rate for each year. The expected value of the interest rate in the third year is 4.40% (0.36x6% + 0.48x5% + 0.16x4%). Explain why the 3-year spot rate is so much lower than this expected value. Use the interest rate factors (value today of $1 delivered in the future) implied by question 1 to value a coupon bond making payments of $500, $500, and $10, 500. Use the interest rate factors to value a mortgage making payments of $10,000 in each of the three years. Modify the tree of question 1 for the 3-year zero coupon bond to incorporate a default risk of 1% per year. What is the value of this bond based on these calculations and what is the spot yield? Consider a binomial tree for interest rates as discussed in class. The interest rate the first period is 4% and rates move up or down by 1% per year; all interest rates are compounded annually. The probability of a move up is 60% (different assumption than in class). All calculations should be done using the full precision of your calculator and computer. It is strongly suggested that you use Excel to make this easier. Answers which are an interest rate or a yield should be expressed with two decimal places showing basis points. Answers which are dollar amounts should include two decimals showing cents, Use the tree to determine the value of 3-year zero coupon bond with face value of $100 incorporating the interest rate uncertainty. Repeat the calculation for a 2-year zero and for a 1-year zero. Use the valuations from the prior questions to determine the spot rate for each year. The expected value of the interest rate in the third year is 4.40% (0.36x6% + 0.48x5% + 0.16x4%). Explain why the 3-year spot rate is so much lower than this expected value. Use the interest rate factors (value today of $1 delivered in the future) implied by question 1 to value a coupon bond making payments of $500, $500, and $10, 500. Use the interest rate factors to value a mortgage making payments of $10,000 in each of the three years. Modify the tree of question 1 for the 3-year zero coupon bond to incorporate a default risk of 1% per year. What is the value of this bond based on these calculations and what is the spot yield