A three-year bond with a face value of 1000 pays coupons semiannually. The bond is redeemable at face value. It is bought at issue at a price to produce an annual yield rate of 10% convertible semiannually. If the term of the bond is doubled and the yield rate remains the same, the purchase price would decrease by 49.

Calculate the amount of a coupon.

• 37
• 46
• 54
• 63
• 74

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

Let [math]r[/math] be the semiannual coupon rate. For the original bond, [math]P=1000 r a_{60.05}+1000 v^6=5075.692 r+746.215[/math]. For the modified bond, [math]P-49=1000 r a_{120.05}+1000 v^{12}=8863.252 r+556.837[/math]. Subtracting the second equation from the first gives [math]49=-3787.56 r+189.378[/math]. The solution is [math]r=0.037[/math] and the coupon is 37 .

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.