At an annual effective interest rate of 6%, the present value of a perpetuity immediate with successive annual payments of 6, 8, 10, 12, ..., is equal to X.

Calculate X.

• 100
• 656
• 695
• 1767
• 2222

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

Solution: B

The present value is

[[math]] 4a_{\overline{4}|0.06} + 2(Ia)_{\overline{\infty}|0.06}=4\,/\,0.06+2(1.06)\,/\,0.06^{2}=655.56. [[/math]]

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