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' backpay. The plaintiff's annual salary for the last two years would have been $43,000 and $46,000, respectively

b. The present value of five years' future salary. You assume the salary will be $51,000 per year

c. $150,000 for pain and suffering

d. $20,000 for court costs.

Assume that the salary payments are equal amounts paid at the end of each month. If the interest rate you choose is an EAR of 6.5 percent, what is the size of the settlement?

PV Value of Annuity:

An annuity is a stream of consistent cash flows that will be paid out for at a specified frequency for a specified period of time. The present value (PV) of an annuity is the current value of its future cash flows. It can be manually computed using the following formula:

PV = P*1-(1+i)^-n / i

Where:

P = Annual payment

i = Discount rate

n = Number of years

Given, the EAR=6.5%, we can find the monthly rate(1+x)^12 - 1 = 0.065

Solving for x, we get ,

x = 0.00526169

ie. 0.5262%

Part a)

PV/current value of two Years' back pay at time, t = 0 (using FVOA formula)

Future value of Annuity of 43000/12 for 12 months up to end of Year. 1 & FV of single Sum for 12 months up to end of Yr.2---at EAR ,

ie.

0.5262% per month (43,000/12 x (1.005262^12-1)/0.005262) x (1+0.005262)^12] = $47,144.05

Future value of Annuity of 46000/12 for 12 months at EAR,

(6.5%/12) = 0.5262% p.m. (46000/12) x (1.005262^12 - 1)/0.005262 = $47,354.92

Part b)

The present value of five years' future salary, at time t = 0

Present value of Annuity of 51000/12 for 60 months at EAR ,

(6.5%/12) = 0.5262% per month 51000/12 x (1- 1.005262^-60)/0.005262 = $218,180

Part c.

Compensation for pain and suffering = $150,000

Part d.

Compensation for Court costs = $20,000

Total size of the settlement(ANSWER) = $482,678.94