Question

A $ 5 comma 000 bond with a coupon rate of 6.6​% paid semiannually has two years to maturity and a yield to maturity of 8.7​%. If interest rates rise and the yield to maturity increases to 9​%, what will happen to the price of the​ bond?

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =2x2

Bond Price =∑ [(6.6*5000/200)/(1 + 8.7/200)^k]     +   5000/(1 + 8.7/200)^2x2

k=1

Bond Price = 4810.99

new price at YTM = 9%

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =2x2

Bond Price =∑ [(6.6*5000/200)/(1 + 9/200)^k]     +   5000/(1 + 9/200)^2x2

k=1

Bond Price = 4784.75

%age change in price =(New price-Old price)*100/old price

%age change in price = (4784.75-4810.99)*100/4810.99

= -0.55%

Bond price decreased by 0.55%