Each of bonds A, B, and C sells for 10,000 and has the same annual effective yield rate and term. The par values and coupon rates are shown below.

Each bond is redeemed at par, and all coupons are paid annually. The par values and coupon rates are shown below.

	Bond A	Bond B	Bond C
Par Value	20,000.00	10,835.58	X
Annual Coupon Rate	0%	4%	3%

Calculate X.

• 12,240
• 12,630
• 13,130
• 13,540
• 14,450

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

Solution: A

Let [math]i[/math] be the yield rate, [math]\mathrm{v}=1 /(1+i)[/math], and let [math]n[/math] be the term. For Bond A, 20,000v [math]v^n=10,000[/math] and so [math]v^n=0.5[/math]. For Bond [math]\mathrm{B}, 10,835 \cdot 58\left(v^n+0.04 a_{n i}\right)=10,000[/math] and so

[[math]] a_{n i}=\left(\frac{10,000}{10,835.58}-0.5\right) / 0.04=10.5721 \text {. } [[/math]]

For Bond C,

[[math]] 10,000=X\left(v^n+0.03 a_{n i}\right)=0.81716 X \Rightarrow X=12,237.51 [[/math]]

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