Can you please explain step by step on how to do this questi

***Can you please explain step by step on how to do this question*** and please show formulas used so i can understand how to do it on my own. thank you.

The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.

Solution

The six months treasury bill provides a return of 6/94 = 6.383% is six months and for annual 6.383*2

= 12.766 % per annum with semiannual compounding or 2in(1.06383) = 12.38% per annum with continous compounding

The 12 month treasury bill is 11/89 = 12.36% or in(1.1236) = 11.65% with continous compounding

for 1.5 year bond we must have

4e^-0.1238*0.5+ 4e^-0.1165*1.0+104e^-1.5R=94.84

R equals to 1.5year zero rate

3.76+3.56+104e^-1.5R=94.84

e^-1.5R= 0.8415

R= 0.115 or 11.5%

for two year bond

5e^-0.1238*0.5+ 5e^-0.1165*1.0+ 5e^-0.115*1.5+105e^-2R=97.12

R is the 2-year zero rate

e^-2R= 0.7977

R = 0.113 or 11.3%