Question
1. You are considering a project which generates $10,000 in 6 months and $20,000 in one year and will run you $26,000 today. You know
1. You are considering a project which generates $10,000 in 6 months and $20,000 in one year and will run you $26,000 today. You know these cash flows are exact. You also have the Treasury yield curve from the Wall Street Journal in front of you and see that the 6-month T-bill is trading at a 4% rate and the one-year T-bond (which pays coupons in 6-months and one-year) is trading at par (100) with a yield of 6%. (Rates are CBE). Should you invest in this project?
2. You have the following incomplete information on yields, forward rates from time t-1 to t, and prices (risk-free, zero-coupon bonds with face amount $100):
Maturity | Yield | Price | Forward Rate |
1 | P1=98.00 | ||
2 | f2=2.50% | ||
3 | y3=2.50% |
Given this information, what is the price of a 3-year, 5%, annual-pay, coupon bond with face amount $1,000? (Please fill in the table as well.)
3. You are doing some bookkeeping concerning a mortgage you took out 10 years ago, $500,000 used to finance a home. You presume it is a 30-year mortgage. You are trying to determine the interest rate (mortgage equivalent yield) on the loan. You know that the monthly payments are $4,023.11. So, you assume therefore that the interest rate on the loan is 9% and call your mortgage broker to check this out. Looking at your numbers, he tells you that you have two things incorrect. First, this was a weird mortgage that did not start with a 30-year maturity. Second, the 9%, it turns out, was purely coincidental. He also tells you that the actual interest paid thus far is 8.78% less than that shown in your calculations based on the 9% interest rate and a $500,000 loan that is the interest paid is .9122 times the figure calculated from your mortgage calculation. From this information, can you determine the actual terms of the mortgage: rate and maturity?
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