You are given the following information regarding Company J.

1. It has a single liability of 1.75 million to be paid 12 years from now.
2. Its asset portfolio consists of a zero-coupon bond maturing in 5 years for 242,180 and a zero-coupon bond maturing in 14 years for X.
3. At an annual effective interest rate of 7%, Company J’s position is fully immunized.

Calculate the present value of the assets less the present value of the liabilities if the annual effective interest rate immediately changes to 4%

• 5,910
• 8,871
• 11,029
• 14,746
• 17,462

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

Solution: A

The PV and duration of the liability payments using [math]7 \%[/math] rate are [math]P V=1,750,000 v^{12}=777,021[/math] and duration 12 .

The amount invested in the 5-year bond is [math]\frac{242,180}{1.07^5}=172,671[/math], Thus, the amount invested in the 14 year bond is [math]777,021-172,671=604,350[/math]. The maturity value of the 14 -year bond is [math]604,350(1.07)^{14}=1,558,337[/math].

The surplus if the interest rate moves to [math]4 \%[/math] is:

[[math]] P V_A-P V_L=\left(\frac{242,180}{1.04^5}+\frac{1,558,337}{1.04^{14}}\right)-\frac{1,750,000}{1.04^{12}}=5,910 [[/math]]

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