Revision as of 08:56, 18 November 2023 by Admin (Created page with "An insurance company has an obligation to pay the medical costs for a claimant. Annual claim costs today are 5000, and medical inflation is expected to be 7% per year. The claimant will receive 20 payments. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today. Calculate the present value of the obligation using an annual effective interest rate of 5%. <ul class="mw-excansopts"><li>87,900</li><li>102,500</li><li>114,60...")
ABy Admin
Nov 18'23
Exercise
An insurance company has an obligation to pay the medical costs for a claimant. Annual claim costs today are 5000, and medical inflation is expected to be 7% per year. The claimant will receive 20 payments. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today.
Calculate the present value of the obligation using an annual effective interest rate of 5%.
- 87,900
- 102,500
- 114,600
- 122,600
- Cannot be determined
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: D.
The present value is
[[math]]
\begin{array}{l}{{5000[1.07 v+1.07^{2} v^{2}+\cdots+1.07^{20} v^{20}]}}\\ {{=5000\frac{1.07 v-1.07^{21} v^{21}}{1-1.07 v}=5000\frac{1.01905-1.48622}{1-1.01905}=122,617.}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.