Question

5. You are given: the 100-day T bill rate is .06. The 150-day T bill rate is .08. What is the “bill parity” or forward discount rate on the future 50-day bill?

Answer 1

Forward discount rate on the future 50 day bill is calculated as:
Forward discount rate={[(1+r2)^(t2)/(1+r1)^(t1)]^1/(t2-t1)} -1

Here, r1 refers to the rate on 100 day T-bill. Here r1 or rate=0.06 and time period t1=100/360 (We divided 360 to convert days to years assuming 360 days a year).

Here, r2 refers to the rate on 150 day T-bill. Here r2 rate=0.08 and time period t2=150/360 (We divided 360 to convert days to years assuming 360 days a year).

Substituting the values, we get
Forward discount rate={[(1+.08)^(150/360)]/[(1+.06)^(100/360)]}^1/(150/360 - 100/360) -1
={[(1.08)^(0.416666667)]/[(1.06)^(0.277777778)]}^1/(0.138888889) -1
={[1.03258679/1.016317508]}^7.199999994 -1
=(1.01600807)^7.199999994 -1
=1.12113919 -1
=0.12113919