Question

What is the percentage price change for a zero coupon bond if its YTM changes from 3.9% to 4.6%? The bond's face value is $1,000 and it matures in 8 years. Use the price determined from the first yield, 3.9%, as the base in the percentage calculation. Round to the nearest tenth of a percent. (e.g., 4.32% = 4.3). ​[Hint: If the price dropped, enter a negative number].

Answer 1

Current price

Bond

K = N

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

k=1

K =8

Bond Price =∑ [(0*1000/100)/(1 + 3.9/100)^k]     +   1000/(1 + 3.9/100)^8

k=1

Bond Price = 736.34

Change in YTM =0.7

Bond

K = N

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

k=1

K =8

Bond Price =∑ [(0*1000/100)/(1 + 4.6/100)^k]     +   1000/(1 + 4.6/100)^8

k=1

Bond Price = 697.82

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

%age change in price = (697.82-736.34)*100/736.34

= -5.23%