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There are two riskless bonds which mature at t = 2.The first is a zero coupon bond that pays a balloon of $ 1,200.The other is a coupon bond with an annual coupon of $100 and a balloon payment of $990.The current yield on a riskless bond that mature in one year is 10%, the annualized yield on a two-year bond is also 10%.
-If the interest rate at t = 1 can be 8% or 12%, what is the percentage price change for the zero coupon bond Answer: change for 8%, change for 12%; round to the nearest figure)?
A)10%, 10%
B)12%, 8%
C)8%, 12%
D)8%, 8%
E)12%, 12%

Question

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There are two riskless bonds which mature at t = 2.The first is a zero coupon bond that pays a balloon of $ 1,200.The other is a coupon bond with an annual coupon of $100 and a balloon payment of $990.The current yield on a riskless bond that mature in one year is 10%, the annualized yield on a two-year bond is also 10%.
-If the interest rate at t = 1 can be 8% or 12%, what is the percentage price change for the zero coupon bond Answer: change for 8%, change for 12%; round to the nearest figure)?
A)10%, 10%
B)12%, 8%
C)8%, 12%
D)8%, 8%
E)12%, 12%

Quizplus · Accepted Answer

For the zero coupon bond:
At t=1, the price will be P = 1200/(1+0.1) = $1,090.91 if the interest rate is 10%
If the interest rate at t=1 is 8%, the price will be P = 1200/(1+0.08) = $1,111.11
If the interest rate at t=1 is 12%, the price will be P = 1200/(1+0.12) = $1,071.43
Therefore, the percentage price changes are:
(change from 10%): (1090.91-1200)/1200 = -9.09%
(change from 8%): (1111.11-1200)/1200 = -6.94%
(change from 12%): (1071.43-1200)/1200 = -10.71%
The largest positive change occurs when the interest rate at t=1 is 8% (i.e. the smallest absolute percentage price change), so the best choice is B.

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