Explanation:

The six-month zero rate is first found from the six-month bill price:

r_{0.5} = 2\ln\left(\frac{100}{98}\right) = 4.0405\%

Then bootstrap the one-year rate using the one-year bill price. The bill pays $1 at 6 months and $101 at 1 year (coupon plus principal):

97 = 1\cdot e^{-0.040405\cdot 0.5} + 101\cdot e^{-R\cdot 1.0}

Solving for $R$ :

R = -\ln\left(\frac{97 - e^{-0.040405\cdot 0.5}}{101}\right) = 5.0564\%

So the correct answer is 5.0564%.

Question 158.1. Bond price using spot rates

The price of a zero-coupon six-month Treasury bill is `$98.00`. The price of a one-year Treasury bill that pays a 2.0% semi-annual coupon is `$97.00`. Using the bootstrap method, what is the one-year Treasury zero (spot) rate expressed in continuous compounding?

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Last updated: April 18, 2026 at 11:32

4.0405%

50.0%

4.9405%

50.0%

5.0564%

5.6564%

Financial Risk Manager Part 1