Joe must pay liabilities of 2000 due one year from now and another 1000 due two years from now. He exactly matches his liabilities with the following two investments:

Mortgage I: A one year mortgage in which X is lent. It is repaid with a single payment at time one. The annual effective interest rate is 6%.

Mortgage II: A two-year mortgage in which Y is lent. It is repaid with two equal annual payments. The annual effective interest rate is 7%.

Calculate X + Y.

• 2600
• 2682
• 2751
• 2825
• 3000

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

Solution: C

Because only Mortgage II provides a cash flow at time two, it must be considered first. The mortgage provides [math]Y/a_{\overline{2}|0.07} = 0.553092Y[/math] at times one and two. Therefore, 0.553092Y = 1000 for Y = 1808.02. Mortgage I must provide 2000 – 1000 = 1000 at time one and thus X = 1000/1.06 = 943.40. The sum is 2751.42.

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