You want to price a 5% coupon semiannual Bond today (Assume $1000 par). The bond will mature in 1 year and 1 month from today. The first coupon will be paid 1 month from now. To price the above bond, you use another 1 year 1 month 6% coupon bond trading at $1040 as a reference. Also, the ZCB yield for 1 month maturity is 4.3% and for 7 month maturity is 4.7%.

a) Estimate the ZCB Spot Rate for the 1 year plus 1 month to maturity with the reference bond and ZCB yields above.

b) Calculate the theoretical value for the 5% coupon bond.