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# extraproblems_8 - ACTSC 231 Extra Problem 1 Consider the...

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Unformatted text preview: ACTSC 231 Extra Problem 1. Consider the following securities: (a) A 26-week \$100 T-bill sells for a price of \$98.50 (b) A 52-week \$100 T-bill (c) A 1 year \$5000 10% government bond with semiannual coupons, sells for a price of \$5194.38. Assuming no arbitrage &nd the price of the 52-week \$100 T-bill. 2. A \$500 bond pays coupons at 8% semiannually and is redeemble at par in 1 year. (a) Use the following spot rates to &nd the price: r : 5 = 7% and r 1 = 7 : 5% , (b) Given the price in part a) &nd the yeild to maturity (IRR). Express the rate as a nominal rate compounded semi-annually. 3. You are given the following quoted prices on Mar. 5, 2003. (The quoted coupon is always annual, but is paid semiannually. I.e. for issue A, a coupon of 4 is paid twice a year) Issue Maturity Coupon Price A Feb 5, 2004 8 103.62 B Aug 5, 2003 98.53 C Feb 5, 2004 96.44 (a) For a bond from issue A, &nd the price if the face value is \$2000. (Note that there are 181 days between Feb 5 ¡ Aug 5) (b) Use the zero coupon bonds (issue B ¡ C) to verify your price in part A. 4. Investor A buys a zero growth stock, which pays annual dividends of \$8, at a price to yield i = 7% . After receiving the 10th dividend investor A sells the stock to investor B to yield i = 8% . (a) Find the IRR for investor A. (b) Find the e/ective annual yield rate earned by investor A if each of the dividends earned i = 5% in a saving account. (c) Repeat part b) assuming an annual growth rate of 1% (e.g. D = 8 ; D 1 = 8 : 08 ;::: ). 5. Given that the e/ective annual spot rate is i ;k = : 048 + : 002 k , &nd f 2 ; 5 : 6. You are given: 6-month T-bills sell for \$95 1 1-year T-bills sell for \$90 1.5-year bonds with 8% coupons paid semiannually sell for \$95.80 2-year bonds with 10% coupons paid semiannually sell for \$98.55 Calculate the 6-month, 1-year, 1.5-year and 2-year annual e/ective spot rates....
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extraproblems_8 - ACTSC 231 Extra Problem 1 Consider the...

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