two 1000 bonds redeemable at par at the end of the same peri

two $1,000 bonds redeemable at par at the end of the same period are bought to yield 4% convertible semiannually. One bonds costs $1,136.78 and has a coupon rate of 5% payable semiannually. The other bond has a coupon rate of 2.5% payable semiannually. Find the price of the second bond.

Solution

Applying the basic formula to the first bond produces
250(1+0.04/2) ^?n= 113.24

(1.02) ^?n = 113.24/250 = 0.45296

n = ?[ln(0.45296) ] / [ln(1.02)]
n = 40.
Now applying the basic formula to the second bond, produces

P = 1000(0.0125) [1 ? (1.02) ^?40]/0.02 + 1000(1.02) ^?40

P = 341.9435 + 452.890
P = $794.83