Two bonds are both redeemable at their par value of 100 in t

Two bonds are both redeemable at their par value of $100 in t years. • Bond A has 3.5% semiannual coupons and costs $88. • Bond B has 4% semiannual coupons and costs $92. • The bonds were purchased to produce the same yield rate. What is the yield rate per annum convertible semiannually? (You might get an effective semiannual rate. Don’t forget to double your result.)

Solution

Given:

Two bonds are both redeemable at their par value of $100 in t years.

A has 3.5% semiannual coupons and costs $88. •

and B has 4% semiannual coupons and costs $92.

A for 1%=88/3.5=880/35=$176/7

B for 1%=92/4=$23

For A per annum 1%=$352/7

   B per annum 1%=$46

the yield rate per annum of A=$352/7*(3.5)=$704

the yield rate per annum of B=$46*(4)=$184

Total A+B yield rate per annum=$888