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Nov 18'23
Exercise
An annuity writer sells an annual perpetuity-immediate for 16,000. The first payment is 1,000 and the payments decrease by r% each year. The annual effective yield rate is 5.7%.
Calculate r.
- 0.52
- 0.55
- 0.62
- 0.73
- 0.91
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 18'23
Solution: B
[[math]]
\begin{aligned} & 16,000=1,000\left(\frac{1}{0.057-(-r / 100)}\right) \\ & 16=\frac{1}{0.057+r / 100} \\ & 0.057+r / 100=\frac{1}{16} \\ & r=0.55\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.