You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following:

(a)
The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $53,000 and $56,000, respectively.
(b)
The present value of five years’ future salary. You assume the salary will be $61,000 per year.
(c) $185,000 for pain and suffering.
(d)
$30,000 for court costs.

Assume the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is an EAR of 8 percent, what is the size of the settlement?

I get that we are actually getting the future value of the 2 years of back pay and the present value of the 5 years of future pay (as an annuity), plus the P&S and court fees added on as a lump sum. What is throwing me off I think is that the question specifically states the EAR. Would you just divide this by 12 because the question states that the salary are equal monthly payments? Or do you need to do something else to get the rate you would actually use in the question?

To calculate the size of the settlement, we need to compute the present value of each component of the award using an effective annual interest rate (EAR) of 8 percent.

(a) The present value of two years' back pay can be calculated as follows:
PV_backpay = $53,000 / (1 + 0.08/12) + $56,000 / (1 + 0.08/12)^2

(b) The present value of five years' future salary can be calculated as follows:
PV_future_salary = $61,000 * [(1 - (1 + 0.08/12)^(-5*12)) / (0.08/12)]

(c) The amount for pain and suffering is $185,000 and does not require discounting.

(d) The court costs are $30,000 and do not require discounting.

Finally, we calculate the total settlement by adding up all the components:
Settlement = PV_backpay + PV_future_salary + $185,000 + $30,000

Please note that the interest rate must be converted to its monthly rate by dividing it by 12. Now, you can substitute the values and compute the settlement amount.

To calculate the size of the settlement, we need to determine the present value (PV) of the back pay, future salary, pain and suffering, and court costs.

Let's start with the back pay:

(a) The plaintiff's annual salary for the last two years would have been $53,000 and $56,000, respectively.

To calculate the present value of two years' back pay, we need to find the present value of each year's salary and sum them up.

PV of Year 1 salary = $53,000 / (1 + 0.08/12)^12*2 = $53,000 / (1.0066667)^24 ≈ $49,694.15
PV of Year 2 salary = $56,000 / (1 + 0.08/12)^12*2 = $56,000 / (1.0066667)^24 ≈ $52,536.42

Total PV of back pay = PV of Year 1 salary + PV of Year 2 salary
= $49,694.15 + $52,536.42 ≈ $102,230.57

Now let's move on to the future salary:

(b) Assuming a salary of $61,000 per year for five years, we need to calculate the present value of these future salary payments.

PV of future salary = $61,000 * [(1 - (1 + 0.08/12)^(-12*5))/ (0.08/12)] = $61,000 * 3.88949 ≈ $237,144.89

Next, let's calculate the amount for pain and suffering:

(c) The plaintiff is seeking $185,000 for pain and suffering.

(d) The court costs are $30,000.

Now we can calculate the total settlement:

Total settlement = PV of back pay + PV of future salary + pain and suffering + court costs
= $102,230.57 + $237,144.89 + $185,000 + $30,000
= $554,375.46

Therefore, the size of the settlement is approximately $554,375.46.