Question

Consider two bonds, a 3-year bond paying an annual coupon of 5.40% and a 10-year bond also with an annual coupon of 5.40%. Both currently sell at face value of $1,000. Now suppose interest rates rise to 10%.

a.	What is the new price of the 3-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bond price

$

b.	What is the new price of the 10-year bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bond price

$

c.	Which bonds are more sensitive to a change in interest rates?
	Long-term bonds Short-term bonds

Answer 1

Price of Bond A

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 5.4%

                YTM or Required rate = 10%

                Time to maturity (n) = 3 years

                Annual coupon C = $54

Let's put all the values in the formula to find the bond current value

P = 54* [{1 - (1 + 0.1) ^ -3}/ (0.1)] + [1000/ (1 + 0.1) ^3]

P = 54* [{1 - (1.1) ^ -3}/ (0.1)] + [1000/ (1.1) ^3]

P = 54* [{1 - 0.75131}/ 0.1] + [1000/ 1.331]

P = 54* [0.24869/ 0.1] + [751.3148]

P = 54* 2.4869 + 751.3148

P = 134.2926 + 751.3148

P = 885.6074

So price of the bond is $885.61

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                Face value = $1000

                Coupon rate = 5.4%

                YTM or Required rate = 10%

                Time to maturity (n) = 10 years

                Annual coupon C = $54

Let's put all the values in the formula to find the bond current value

P = 54* [{1 - (1 + 0.1) ^ -10}/ (0.1)] + [1000/ (1 + 0.1) ^10]

P = 54* [{1 - (1.1) ^ -10}/ (0.1)] + [1000/ (1.1) ^10]

P = 54* [{1 - 0.38554}/ 0.1] + [1000/ 2.59374]

P = 54* [0.61446/ 0.1] + [385.54366]

P = 54* 6.1446 + 385.54366

P = 331.8084 + 385.54366

P = 717.35206

So price of the bond is $717.35

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Long term bond is more sensitive, look at the price change, long term bond price change has decreased more than the first bond.

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