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 |
A $51,000, 88% bond redeemable at 104 with semi-annual coupons bought eleven years before matu...
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