Question

Bond RTY.AF has a 5 percent coupon, makes semiannual payments, currently has 18 years remaining to maturity, and is currently priced at par value. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond RTY.AF? Be sure to include the sign, especially if the bond price falls and the percentage change is negative. (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Answer 1

Percentage change in price For Bond RTY.AF

Step 1:

Price of bond before rise in interest rate is at par value, let par value be $1,000

The present interest rate should be equal to coupon rate because bond is priced at par.

Interest rate = i = 5%

Value of bond before rise in interest rate = Par value = $1000

Step 2:

Calculate the price of the bond after rise in interest rate i.e. by 2%:

Revised interest rate = Coupon rate or Interest rate + 2% = 5% + 2% = 7%

Step 3:

i = current interest / Frequency of coupon = 7%/2 = 3.5%

Face value = FV = $1,000

N = Total number of periods = Total years x Frequency of coupon = 18 x 2 = 36

PMT = Coupon payment = Face value x Coupon rate / Frequency of coupon = 1000 x 5% / 2 = $25

Present value of bond = PV = ?

Step 4:

Value of bond after rise in interest rate:

Formula for bond value:

PV = PMT x ((1-((1+i)^-N)) / i) + (FV/(1+i)^N) =

PV = (25* ((1-(1+3.5%)^-36)/3.5%) + 1000/(1+3.5%)^36)

PV = 289.8327166 + 507.2623453

PV = 797.0950619

Step 5:

Percentage change in price of bond = ((Value of bond after rise in interest - Value of bond before rise in interest rate) / Value of bond before rise in interest rate) x 100

Percentage change in price of bond = ((797.0950619 - 1000) / 1000) x 100

Percentage change in price of bond = (-202.9049381 / 1000) x 100

Percentage change in price of bond = -20.2904938

Percentage change in price of bond = -20.29 Or -20.29 percent