Each bond identified in the table has semiannual coupon paym

Each bond identified in the table has semiannual coupon payments. Use the data in the table to answer the following two questions. +- Determine the zero rates for maturities of 6 months, 1 year, and 18 months expressed in terms of continuous compounding.+ Determine the forward rate based on annual compounding for the period of time between one year and 1.5 a. b. years Time to Annual Bond NumberPrincipal Bond maturity*Coupon rate Bond Price 100 100 100 (years) 0.54 1.0 96.6 98.8\' 02.1*

Solution

1.
96.6=4%*100/2*e^(-6month rate*0.5)+100*e^(-6month rate*0.5)
=>6month rate=10.8788%
2.
98.8=7%*100/2*e^(-6month rate*0.5)+7%*100/2*e^(-1year rate*1)+100*e^(-1year rate*1)
=>1 year rate=8.0599%
3.
102.1=11%*100/2*e^(-6month rate*0.5)+11%*100/2*e^(-1year rate*1)+11%*100/2*e^(-1.5year rate*1.5)+100*e^(-1.5year rate*1.5)
=>1.5 year rate=9.2607%

4.
annual compounding 1 year rate=e^(8.0599%)-1=8.3936%
annual compounding 1.5 year rate=e^(9.2607%)-1=9.7031%
Hence, forward rate between 1 year and 1.5 years=(((1+9.7031%)^1.5)/((1+8.3936%)^1))^(1/0.5)-=12.3698%