Revision as of 20:28, 18 November 2023 by Admin (Created page with "A perpetuity-due with annual payments is priced at X based on an annual effective interest rate of 7%. The amount of the first payment is 350. Each payment, from the second through the thirtieth, is 3% larger than the previous payment. Starting with the 31st payment, each payment is equal to the 30th payment. Calculate X. <ul class="mw-excansopts"><li>7508</li><li>7855</li><li>7925</li><li>7971</li><li>8033</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A perpetuity-due with annual payments is priced at X based on an annual effective interest rate of 7%. The amount of the first payment is 350. Each payment, from the second through the thirtieth, is 3% larger than the previous payment. Starting with the 31st payment, each payment is equal to the 30th payment.
Calculate X.
- 7508
- 7855
- 7925
- 7971
- 8033
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: E
Break this into two parts – the first 30 increasing payments and the remaining level perpetuity.
[[math]]350\left[\frac{1-\left(\frac{1.03}{1.07}\right)^{30}}{0.07-0.03}\right](1.07)+v^{29}\left(\frac{1}{0.07}\right) 350(1.03)^{29}=8033.38[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.