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: (a) The present value of two years’ back pay. 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) How do you find this answer on a BAII Plus Calculator?

Answer 1

Step 1: Calculate APR with the use of EAR

The value of APR with the use of EAR is determined as below:

APR = Number of Months*[(1+Effective Rate of Interest)^1/12 - 1]

Substituting values in the above formula, we get,

APR = 12*[(1+6.5%) -1] = 6.31%

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Step 2: Calculate Future Value of Annuity Today of the Back Pay from 2 Years Ago

The future value annuity of the back pay from 2 years ago can be calculated with the use of FV (Future Value) function/formula of EXCEL/Financial Calculator. The function/formula for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Payment and PV = Present Value.

Here, Rate = 6.31%/12, Nper = 12, PMT = 43,000/12 and PV = 0

Using these values in the above function/formula for FV, we get,

Future Value of Annuity Today of the Back Pay from 2 Years Ago = FV(6.31%/12,12,43000/12,0)*(1+6.5%) = $47,143.80

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Step 3: Calculate Value Today of Last Year's Back Pay

The future value today of the last year's back pay can be calculated with the use of FV (Future Value) function/formula of EXCEL/Financial Calculator. The function/formula for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Payment and PV = Present Value.

Here, Rate = 6.31%/12, Nper = 12, PMT = 46,000/12 and PV = 0

Using these values in the above function/formula for FV, we get,

Future Value of Today of Last Year's Back Pay = FV(6.31%/12,12,46000/12,0) = $47,354.83

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Step 4: Calculate Present Value of Future Salary of 5 Years

The present value of future salary can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value.

Here, Rate = 6.31%/12, Nper = 12*5 = 60, PMT = 51,000/12 and FV = 0

Using these values in the above function/formula for FV, we get,

Present Value Today of Future 5 Year Salary = PV(6.31%/12,60,51000/12,0) = $218,181.90

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Step 5: Calculate Size of Settlement

The value of settlement is determined as below:

Size of Settlement = Future Value of Annuity Today of the Back Pay from 2 Years Ago + Future Value of Today of Last Year's Back Pay + Present Value Today of Future 5 Year Salary + Pain and Suffering + Court Costs = 47,143.80 + 47,354.83 + 218,181.90 + 150,000 + 20,000 = $482,680.53

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Notes:

There can be a slight difference in final answer on account of rounding off values.