Revision as of 19:37, 18 November 2023 by Admin (Created page with "A perpetuity-immediate pays 20 for 10 years, decreases by 1 per year for 19 years, and then pays 1 per year thereafter. At an annual effective interest rate of 6%, the present value is equal to X. Calculate X. <ul class="mw-excansopts"><li>208</li><li>213</li><li>218</li><li>223</li><li>228</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A perpetuity-immediate pays 20 for 10 years, decreases by 1 per year for 19 years, and then pays 1 per year thereafter. At an annual effective interest rate of 6%, the present value is equal to X.
Calculate X.
- 208
- 213
- 218
- 223
- 228
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
[[math]]
\begin{aligned} 2000 & =X(1.08)^{14}+X(1.03)(1.08)^{13}+X(1.03)^2(1.08)^{12}+\cdots+X(1.03)^{14} \\ & =X \frac{1.08^{14}-1.03^{15} / 1.08}{1-1.03 / 1.08} \\ & =32.284 X \\ X & =61.95\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.