Suppose the prices of one-year, two-year, and three-year zero coupon bonds each with a par value...

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Question

Suppose the prices of one-year, two-year, and three-year zero coupon bonds each with a par value...

Suppose the prices of one-year, two-year, and three-year zero coupon bonds each with a par value of $100 are $90, $80, and $70, respectively.

Compute the three spot rates.

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Answer 1

Answer #1

The formula for the zero-coupon bond is -

Price = Par Value /(1+ Spot Rate )ⁿ

n = number of periods

Given that

Par Value of all three bonds = $100

1. 90 = 100/(1+s₁)¹

s₁ = one year spot rate = 1/9 = 11.11%

2. 80 = 100/(1+s₂)²

s₂ = two year spot rate = 1.1180-1 = 11.80%

3. 70 = 100/(1+s₃)³

s₃ = three year spot rate = 1.2162-1 = 12.62%

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Answer 2

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