Question

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: (1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $51,000 and $54,000, respectively. (2) The present value of five years’ future salary. You assume the salary will be $58,000 per year. (3) $100,000 for pain and suffering. (4) $30,000 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 9 percent, what is the size of the settlement? (

Answer 1

EAR = 9%

present value of annuity = payment per period * [ 1 - (1+i)^-n ]/i

future value of annuity = payment per period * [(1+i)^n - 1]/i

(1+ monthly rate)^12 - 1 = 9%

=>

monthly rate = 0.7207%

size of settlement

= present value of back pay + present value + future pay + 100000 + 30000

= 54000/12 * [(1+0.7207%)^12 -1]/0.7207%

+ 51000/12 * [(1+0.7207%)^12 -1]/0.7207% * (1+0.7207%)^12

+ 58000/12 * [1 -(1+0.7207%)^-60]/0.7207%

+ 100000 + 30000

= 56192.744 + 57847.085 + 234763.119 + 100000 + 30000

= 478802.95