Question

Consider a one-year maturity, $100,000 face value bond that pays a 6 percent fixed coupon annually.

If the bond is selling at par, what is the percentage price change for the bond if interest rates increase 50 basis points from 6 percent?

please show all works

Answer 1

Change in YTM =0.5

Bond

K = N

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

k=1

K =1

Bond Price =∑ [(6*100000/100)/(1 + 6.5/100)^k]     +   100000/(1 + 6.5/100)^1

k=1

Bond Price = 99530.52

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

%age change in price = (99530.52-100000)*100/100000

= -0.47%