Prosperity Insurance sells a two-year annuity with equal payments at the end of each year. The price of this annuity is 9297. Prosperity Insurance creates a portfolio made up of a one-year zero- coupon bond and a two-year zero-coupon bond to immunize this annuity. The company uses an annual effective interest rate of 5% to vaue its assets and liabilities.

Calculate the amount invested today in the two-year zero-coupon bond

• 3769
• 4535
• 4762
• 5000
• 9297

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

Solution: B

[[math]] \begin{aligned} & 9297=P a_{20.05} \\ & P=5000 \\ & \frac{5000}{1.05^2}=4535.12 \end{aligned} [[/math]]

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