A $5,000?, 5% bond redeemable at par with semi-annual coupons bought eleven years before maturity to yield 9% compounded? semi-annually is sold three years before maturity at 99.25. Find the gain or loss on the sale of the bond.

Calculation of Purchase price:

Par value of bond = 5000

semiannual coupon amount = par value*coupon rate/number of semiannual period in a year

=5000*5%/2

=125

Total years to maturity = 11

semiannual years to maturity (n) =11*2 =22

Yield at time of purchase =9%

semiannual yield (i) =9%/2 = 0.045

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(125*(1-(1/(1+0.045)^22))/0.045) + (5000/(1+0.045)^22)

=3621.557524

Calculation of gain or loss on sale of bond:

Purchase price =3621.557524

Sale price = 99.25 means 99.25% of face value

=5000*99.25%

=4962.5

Gain or loss on sale of bond = Sale price - purchase price

=4962.5-3621.557524

=1340.942476

so Gain is $1340.94 on sale of bond