Question

You are currently six years away from the date you planned to retire. Unfortunately, you were in a work-related accident two years ago and have not been able to work since. You went to court and the jury decided in your favor and ruled that the defendant must pay for your past and future lost wages and pain and suffering costs of $250,000. The judge assumes the pain and suffering was experienced two years ago and must be converted into today’s dollars. It has been determined that your salary two years ago would have been $100,000 and was expected to grow 4% the following two years and then remain constant until retirement. If the defendant is ordered to make the entire payment today, how much will you receive today if the effective annual rate is 8% and all your salary payments come in monthly installments?

Answer 1

Monthly Salary two years ago is 100,000/12 = $8,333.33. Future value of salary for the last two years, assuming an interest rate of 8%, with 4% increment is $229,070. Future Value = Salary*(1+8%/12)^(Month-24).

Month	Salary	Future Value
1	8,667	10,098
2	8,667	10,031
3	8,667	9,964
4	8,667	9,898
5	8,667	9,833
6	8,667	9,768
7	8,667	9,703
8	8,667	9,639
9	8,667	9,575
10	8,667	9,512
11	8,667	9,449
12	8,667	9,386
13	9,013	9,697
14	9,013	9,633
15	9,013	9,569
16	9,013	9,505
17	9,013	9,442
18	9,013	9,380
19	9,013	9,318
20	9,013	9,256
21	9,013	9,195
22	9,013	9,134
23	9,013	9,073
24	9,013	9,013
Total		229,070

As monthly salary 9,013 remains constant for next 6 years till retirement, Present value of these future cashflows is calculated from excel formula PV(8%/12,72,-9,013,0) i.e. $514,071.

Therefore, current day value for past & future salaries is $229,070+$514,071 = $ 743,141. And the defendant has to pay penalty of $250,000 in current day value for pain & suffering is $250,000*(1+8%/12)^24 = $270,750 (assuming monthly compounding). Therefore, total payment to be made = $743,141 + $270,750 = $ 1,013,891.