Question

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.)

Answer 1

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