Ch.13_Solution_Manual_Ed.1_v6_

# Ch.13_Solution_Manual_Ed.1_v6_ - Exercise 13.1 Exercise...

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Exercise 13.1 Exercise 13.1, Solution 1: Face value, FV = \$1000.00, n = 2 × 5 = 10, Coupon rate, b === 0.015 per half-year PMT = FV × b = 1000.00 × 0.015 = \$15.00 Yield, i === 0.0125 per half-year purchase price = PV PMT + PV Face Value = + =+ 1000(1+0.0125) -10 = 140.182888… + 883.180926… = \$1023.363815… = \$1023.36 Premium = Purchase Price – Face Value=1023.36 – 1000.00 = \$23.36 Therefore, she paid \$1023.36 for this bond, and the premium was \$23.36. Exercise 13.1, Solution 3: Face value, FV = \$25,000.00, n = 2 × 10 = 20, Coupon rate, b === 0.0225 per half-year PMT = FV × b = 25,000.00 × 0.0225 = \$562.50 Yield, i === 0.015 per half-year purchase price = PV PMT + PV Face Value = + =+ 25,000(1+0.015) -20 = 9657.359317… + 18,561.76046… = \$28,219.11977… = \$28,219.12 Premium = Purchase Price – Face Value=28,219.12 – 25,000.00 = \$3219.12 Therefore, the issue price is \$28,219.12, and the premium is \$3219.12. Exercise 13.1, Solution 5: Face value, FV = \$10,000.00, n = 2 × 3 = 6, Coupon rate, b === 0.0175 per half-year PMT = FV × b = 10,000.00 × 0.0175 = \$175.00 Yield, i === 0.00875 quarterly c = Number of compounding periods per year Number of payments per year = i 2 = (1 + i ) c – 1 = (1 + 0.00875 ) (4/2) – 1 = 0.017576… semi-annually purchase price = PV PMT + PV Face Value = + =+ 10,000(1+0.017576. ..) -6 = 988.3180464… + 9007.358062… = \$9995.676109. .. = \$9995.68 Discount = Face Value – sale Price = 10,000.00 – 9995.68 = \$4.32 Therefore, the purchase price is \$9995.68, and the discount is \$4.32. Exercise 13.1, Solution 7: Purchasing the bond Face value, FV = \$1000.00, n = 2 × 5 = 10,
Coupon rate, b = = = 0.025 per half-year PMT = FV × b = 1000.00 × 0.025 = \$25.00 Yield, i = = = 0.03 per half-year purchase price = PV PMT + PV Face Value = + = + 1000(1+0.03) -10 = 213.255070… + 744.093914… = \$957.348985… = \$957.35 Selling the bond n = 2 × 3 = 6 Yield, i = = = 0.02 per half-year sale price = PV PMT + PV Face Value = + = + 1000(1+0.02) -6 = 140.035772… + 887.971382… = \$1028.007154… = \$1028.01 Gain = sale price – purchase price = 1028.01 – 957.35 = \$70.66 Therefore, her gain on the bond was \$70.66. Exercise 13.1, Solution 9: Redemption date: July 01, 2020 Interest dates: January 01 and July 01 every year Purchase date: September 10, 2015 Previous interest date: July 01, 2015 Next interest date: January 01, 2016 Time period from previous interest date to redemption date = July 01, 2015 to July 01, 2020 = 5 years Face value, FV = \$10,000.00, n = 2 × 5 = 10, Coupon rate, b === 0.02325 per half-year PMT = FV × b = 10,000.00 × 0.02325 = \$232.50 Yield, i === 0.0275 per half-year purchase price = PV PMT + PV Face Value = + =+ 10,000(1+0.0275) -10 = 2008.817708… + 7623.979055… = \$9632.796763… Assume 't' to be the fractional time period from the previous interest date to purchase date. t

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Ch.13_Solution_Manual_Ed.1_v6_ - Exercise 13.1 Exercise...

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