The present value of a perpetuity-due with payments of X at the beginning of each 3-year period with an annual effective interest rate of 7% is 735.

Calculate X.

• 135
• 138
• 141
• 144
• 147

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

Solution: A

The 3-year interest rate is [math]1.07^3-1=0.225043[/math]

Then,

[[math]] 735=X\ddot{a}_{\overline{\infty}|0.225043}=X\,\frac{1.225043}{0.225043}=5.443595X\,\,\,\mathrm{and}\,X=735/5.443595=135.02. [[/math]]

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