Revision as of 12:07, 18 November 2023 by Admin (Created page with "An insurance company sells an annuity that provides 20 annual payments, with the first payment beginning one year from today and each subsequent payment 2% greater than the previous payment. Using an annual effective interest rate of 3%, the present value of the annuity is 200,000. Calculate the amount of the final payment from this annuity. <ul class="mw-excansopts"><li>11,282</li><li>16,436</li><li>16,765</li><li>19,784</li><li>24,162</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
An insurance company sells an annuity that provides 20 annual payments, with the first payment beginning one year from today and each subsequent payment 2% greater than the previous payment. Using an annual effective interest rate of 3%, the present value of the annuity is 200,000.
Calculate the amount of the final payment from this annuity.
- 11,282
- 16,436
- 16,765
- 19,784
- 24,162
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
The initial payment, X is
[[math]]
\begin{aligned}
200,000 &=X\left({\frac{1}{1.03}}+{\frac{1.02}{1.03^{2}}}+\dots+{\frac{1.02^{19}}{1.03^{2}}}\right)=X{\frac{1/1.03-1.02^{20}\;/1.03^{21}}{1-1.02/1.03}}=17.7267 \\
X &= 11,282.42.
\end{aligned}
[[/math]]
The final payment is 11,282.42 (1.02)19 =16, 436.36.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.