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actsc231A6_part1

# actsc231A6_part1 - (5 A 15-year mortgage is repaid with...

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ACTSC231 ASSIGNMENT 6 PART 1, DUE TUESDAY 27, JULY 27 (1) We are given the following prices for bonds paying annual coupons maturity annual coupon price per \$100 of par 1 10% 106.7961 2 2% 94.4588 3 8% 100.7571 Find the price of a 3-year bond with annual coupons of 12% and \$100 of par value. (2) The prices of zero-coupon bonds with maturity from 1 year to 5 year are 97 . 0874 , 90 . 7029 , 81 . 6298 , 73 . 5030 , 64 . 2529 . Determine the value of f [3 , 4] , the annual effective forward rate applicable from time 3 to time 4. (3) A 4-year bond pays annual coupons of 8%. The annual effective yield on the bond is 5%. find the modified duration of the bond. (4) a 22-year bond pays 7% annual coupons and has a current price of \$81.12. The annual effective yield on the bond is 9%. The Macaulay duration of the bond is 10.774. Estimate the new price if the yield falls to 8.95%.
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Unformatted text preview: (5) A 15-year mortgage is repaid with level monthly payments. the yield is 12% compounded monthly. Calculate the Macaulay duration of the mortgage. (6) The modiﬁed duration of an 8-year bond is 5.35 and its convexity is 39.19. Es-timate the percentage change in the price of the bond if its yield increases by 63 basis points. (7) An insurance company has committed to make a payment of 100,000 in 10 years. In order to fund this liability, the company has invested 27,919.74 in a 5-year zero-coupon bond and 27,919.74 in a 15-year zero-coupon bond. The annual eﬀective yield on all assets and liabilities is 6%. Determine whether the company’s position is immunized. Practice problems : Problem 8.3.1, 8.3.3, 8.3.5 (page 382), Chapter 8 review prob-lems: 6 (page 390) 1...
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