Chapter 4 solutions - CHAPTER 4 Interest Rates Practice...

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CHAPTER 4 Interest Rates Practice Questions Problem 4.1. A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding? (a) The rate with continuous compounding is 0 14 4ln 1 0 1376 4 . + = . ÷ or 13.76% per annum. (b) The rate with annual compounding is 4 0 14 1 1 0 1475 4 . + - = . ÷ or 14.75% per annum. Problem 4.2. What is meant by LIBOR and LIBID. Which is higher? LIBOR is the London InterBank Offered Rate. It is calculated daily by the British Bankers Association and is the rate a AA-rated bank requires on deposits it places with other banks. LIBID is the London InterBank Bid rate. It is the rate a bank is prepared to pay on deposits from other AA-rated banks. LIBOR is greater than LIBID. Problem 4.3. The six-month and one-year zero rates are both 10% per annum. For a bond that has a life of 18 months and pays a coupon of 8% per annum (with semiannual payments and one having just been made), the yield is 10.4% per annum. What is the bond’s price? What is the 18- month zero rate? All rates are quoted with semiannual compounding. Suppose the bond has a face value of $100. Its price is obtained by discounting the cash flows at 10.4%. The price is 2 3 4 4 104 96 74 1 052 1 052 1 052 + + = . . . . If the 18-month zero rate is R , we must have 2 3 4 4 104 96 74 1 05 1 05 (1 2) R + + = . . . + / which gives 10 42 R = . %.
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Problem 4.4. An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with a) annual compounding, b) semiannual compounding, c) monthly compounding and d) continuous compounding. (a) With annual compounding the return is 1100 1 0 1 1000 - = . or 10% per annum. (b) With semi-annual compounding the return is R where 2 1000 1 1100 2 R + = ÷ i.e., 1 1 1 1 0488 2 R + = . = . so that 0 0976 R = . . The percentage return is therefore 9.76% per annum. (c) With monthly compounding the return is R where 12 1000 1 1100 12 R + = ÷ i.e. 12 1 1 1 1 00797 12 R + = . = . ÷ so that 0 0957 R = . . The percentage return is therefore 9.57% per annum. (d) With continuous compounding the return is R where: 1000 1100 R e = i.e., 1 1 R e = . so that ln1 1 0 0953 R = . = . . The percentage return is therefore 9.53% per annum. Problem 4.5. Suppose that zero interest rates with continuous compounding are as follows: Maturity (months) Rate (% per annum) 3 8.0 6 8.2 9 8.4 12 8.5 15 8.6 18 8.7 Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters. The forward rates with continuous compounding are as follows to
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Qtr 2 8.4% Qtr 3 8.8% Qtr 4 8.8% Qtr 5 9.0% Qtr 6 9.2% Problem 4.6. Assuming that zero rates are as in Problem 4.5, what is the value of an FRA that enables the
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Chapter 4 solutions - CHAPTER 4 Interest Rates Practice...

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