A store purchased couch #1 for X two months ago and plans to sell it for 1500 six months from today. The same store purchases couch #2 for X today and plans to sell it for 1500 four months from today. The annual force of interest is a constant 10%. The current value of the store’s cash flows from the purchase and sale of couch #2 is 260.

Calculate the current value of the store’s cash flows from the purchase and sale of couch #1.

• 216
• 218
• 256
• 260
• 307

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

Solution: A

The current value for couch [math]\# 2[/math] is [math]260=1500 e^{-0.1(4 / 12)}-X=1450.82-X \Rightarrow X=1190.82[/math]. The current value for couch [math]\# 1[/math] is [math]1500 e^{-0.1(6 / 12)}-1190.82 e^{0.1(2 / 12)}=1426.84-1210.83=216[/math].

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