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.

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.