Question

# A ​\$51,000, 88​% bond redeemable at 104 with​ semi-annual coupons bought eleven years before maturity to...

A ​\$51,000, 88​% bond redeemable at 104 with​ semi-annual coupons bought eleven years before maturity to yield 9% compounded​ semi-annually is sold three years before maturity at 102.25. Find the gain or loss on the sale of the bond.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

 1) Purchase price of the bond is the PV of the expected cash flows from the bond from the time it was purchased till its maturity. The cash flows are: *The redeemable value of \$53040 at t11 and *the semi-annual coupons of \$2040 for 22 half years, which constitute and annuity. The discount rate is the market interest rate of 4.5% per half year. Hence, the purchase price = 53040/1.045^22+2040*(1.045^22-1)/(0.045*1.045^22) = \$ 48,259.56 2) Sale value = 51000*102.25% = \$ 52,147.50 3) Loss on sale = 52147.50-48259.56 = \$    3,887.94

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