An insurance company must pay liabilities of 99 at the end of one year, 102 at the end of two years and 100 at the end of three years. The only investments available to the company are the following three bonds. Bond A and Bond C are annual coupon bonds. Bond B is a zero-coupon bond.

Bond	Maturity (in years)	Yield-to-Maturity (Annualized)	Coupon Rate
A	1	6%	7%
B	2	7%	0%
C	3	9%	5%

All three bonds have a par value of 100 and will be redeemed at par.

Calculate the number of units of Bond A that must be purchased to match the liabilities exactly.

• 0.8807
• 0.8901
• 0.8975
• 0.9524
• 0.9724

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

Solution: A

Let N be the number of shares bought of the bond as indicated by the subscript.

[[math]] \begin{array}{l}{{N_{C}(105)=100,N_{C}=0.9524}}\\ {{N_{B}(100)=102-0.9524(5),N_{B}=0.9724}}\\ {{N_{A}(107)=99-0.9524(5),N_{A}=0.8807}}\end{array} [[/math]]

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