Project P requires an investment of 4000 today. The investment pays 2000 one year from today and 4000 two years from today. Project Q requires an investment of X two years from today. The investment pays 2000 today and 4000 one year from today. The net present values of the two projects are equal at an annual effective interest rate of 10%.

Calculate X.

• 5400
• 5420
• 5440
• 5460
• 5480

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

Solution: D

Equate net present values:

[[math]] \begin{array}{c}{{-4000+2000 v+4000 v^{2}=2000+4000 v-X v^{2}}}\\ {{\frac{4000+X}{1.1}=6000+\frac{2000}{1.1}}} \\ X= 5460. \end{array} [[/math]]

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