Question

Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has five years to maturity, whereas Bond Dave has 16 years to maturity.

If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Percentage change in price of Bond Sam	%
Percentage change in price of Bond Dave	%

Answer 1

price of coupon = Coupon payment per period * [1-(1+i)^-n]/i + par value/(1+i)^n

i = interest rate per period

n = number of periods

At par value , Yield to maturity is equal to coupon rate , So YTM = 8%

Price before raise

Price of S = 1000

Price of D = 1000

Price after increase

YTM = 10%

Price of S = (80/2) * [1-(1+0.1/2)^-10]/(0.1/2) + 1000/(1+0.1/2)^10

= 922.78

Price of D = (80/2) * [1-(1+0.1/2)^-32]/(0.1/2) + 1000/(1+0.1/2)^32

=841.97

Percentage Change in S = (922.78-1000)/1000

= -7.72%

Percentage Change in D = (841.97-1000)/1000

= -15.80%