Question

A ​$7,000​, 10​% bond redeemable at par with​ semi-annual coupons bought nine years before maturity to yield 9% compounded​ semi-annually is sold four years before maturity at 93.625.

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

Let us first calculate the purchase price for bond which is given by

P0= I(1-(1+r)^-p)/r + FV/(1+r)^p

Where

F = face value =100 (assumed as this is not given in the question)

I = semiannual coupon amout = F× 10%=100×10%× 1/2=5$

r = semiannual annual yield= 9%/2= 4.5%

p = semiannual periods during time to maturity = 9 years ×2= =18

Therefore

P0= 5(1-1.045^-18)/.045 +100/(1.045)^18 = 106.08$

Sale price S= 93.625

Loss on sale = 93.625-106.08= 12.455$

Bonds were bought 9 years before but sold 4 years before maturity that means bonds were held for 9-4=5 years

Hence holding period return or yield is given by

Y/2= (I+(S-P0)/n)/((S+P0)/2)

Where n=semiannual periods in holding period = 5×2=10

Y= annualised return =??

Y/2=(5+(93.625-106.08)/10)/((93.625+106.08)/2) =7.52%