As of 12/31/2013, an insurance company has a known obligation to pay 1,000,000 on 12/31/2017. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling 822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/2017. The maturity value of the bond equals the par value.

Consider two reinvestment interest rate movement scenarios effective 1/1/2014. Scenario A has interest rates drop by 0.5%. Scenario B has interest rates increase by 0.5%.

Determine which of the following best describes the insurance company’s profit or (loss) as of 12/31/2017 after the liability is paid.

• Scenario A – 6,610, Scenario B – 11,150
• Scenario A – (14,760), Scenario B – 14,420
• Scenario A – (18,910), Scenario B – 19,190
• Scenario A – (1,310), Scenario B – 1,320
• Scenario A – 0, Scenario B – 0

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

Solution: D

Under either scenario, the company will have 822,703(0.05) = 41,135 to invest at the end of each of the four years. Under Scenario A these payments will be invested at 4.5% and accumulate to

[[math]]41,135 s_{\overline{4}|0.055} = 41,135(4.2782) = 175,984.[[/math]]

Adding the maturity value produces 998,687 for a loss of 1,313. Note that only answer D has this value. The Scenario B calculation is

[[math]]41,135s_{\overline{4}|0.055}=41,135(4.3423)=178,621+822,703-1,000,000=1,324. [[/math]]

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