Answer: b) 2.75 basis points

Let the 6-year discount factor be: \[ df(6)=0.820 \] ### 1) Implied continuously compounded spot rate For continuous compounding: \[ df(t)=e^{-rt} \] So: \[ r = -\frac{\ln(0.820)}{6} \approx 0.03314 = 3.314\% \] ### 2) Implied semi-annual spot rate For semi-annual compounding: \[ df(t)=\frac{1}{\left(1+\frac{y}{2}\right)^{2t}} \] Thus: \[ 0.820 = \frac{1}{\left(1+\frac{y}{2}\right)^{12}} \] \[ 1+\frac{y}{2} = \left(\frac{1}{0.820}\right)^{1/12} \] \[ y \approx 3.342\% \] ### 3) Difference \[ 3.342\% - 3.314\% = 0.028\% = 2.8 \text{ bps} \] The nearest answer is **2.75 basis points**.

Author: Manit Arora