Revision as of 19:07, 18 November 2023 by Admin (Created page with "A perpetuity-immediate with annual payments is priced at X based on an annual effective interest rate of 10%. The amount of the first payment is 14,000. Each payment, from the second through the twentieth, is 4% larger than the previous payment. The 21st payment and each subsequent payment will be 1% larger than the previous payment. Calculate X. <ul class="mw-excansopts"><li>185,542</li><li>191,834</li><li>206,540</li><li>208,508</li><li>212,823</li></ul> {{soacopyri...")
ABy Admin
Nov 18'23
Exercise
A perpetuity-immediate with annual payments is priced at X based on an annual effective interest rate of 10%. The amount of the first payment is 14,000. Each payment, from the second through the twentieth, is 4% larger than the previous payment. The 21st payment and each subsequent payment will be 1% larger than the previous payment.
Calculate X.
- 185,542
- 191,834
- 206,540
- 208,508
- 212,823
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
The PV of the first twenty payments is:
[[math]]
14,000\left(\frac{1-\left(\frac{1.04}{1.10}\right)^{20}}{0.10-0.04}\right)=157,337.48
[[/math]]
The PV of the remaining payments starting at time 21 is:
[[math]]
14,000(1.04)^{19}(1.01)\biggl(\frac{1}{0.10-0.01}\biggr)(1.10)^{-20}=49.202.44
[[/math]]
Total equals 206,539.92.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.