The 6-months risk-free zero rate is 2.84%, and the one-year zero rate is 3.17%. Assuming no-arbitrage, the yield-to-maturity on a $1,000 par of a one-year, 12% Treasury bond, that pays $60 after 6 months and $1060 after one-year, must be
A) Greater than 0% and less than 2.84%
B) Greater than 2.84% and less than 3.17%
C) Greater than 3.17% and less than 6.01%
D) 6.01%

Question

The 6-months risk-free zero rate is 2.84%, and the one-year zero rate is 3.17%. Assuming no-arbitrage, the yield-to-maturity on a $1,000 par of a one-year, 12% Treasury bond, that pays $60 after 6 months and $1060 after one-year, must be 
A) Greater than 0% and less than 2.84%
B) Greater than 2.84% and less than 3.17%
C) Greater than 3.17% and less than 6.01%
D) 6.01%

Quizplus · Accepted Answer

To find the yield-to-maturity on the Treasury bond, we can solve for the interest rate that will make the present value of the bond's cash flows equal to its current price. Using the given information, we can calculate the present value of the bond's cash flows as follows:
PV = 60/(1+0.0284/2) + 1060/(1+0.0317)
PV = $1,008.02
To solve for the yield-to-maturity, we can use trial and error, or we can use a financial calculator or Excel's RATE function. The yield-to-maturity is approximately 3.01%.
Since the 3.01% yield-to-maturity is greater than the 2.84% six-month zero rate and less than the 3.17% one-year zero rate, the answer is B.

The 6-Months Risk-Free Zero Rate Is 2