Question

A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $220,000 a year for the next 25 years. The attorney for the plaintiff's estate argues that the lost income should be discounted back to the present at 5 percent. The lawyer for the defendant's insurance company argues for a discount rate of 13 percent. What is the difference between the present value of the settlement at 5 percent and 13 percent? Compute each one separately. Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Present Value PV at 5% rate PV at 13% rate Difference

Answer 1

Present value of annuity=PV_{​​​​​A}=A{1-(1+i)^-n)÷i}

Present value at 5% =

$220,000{ 1 - ( 1 +0.05)^-25÷0.05)} = $3,100,667.80

Present value at 13% =

$220,000{1-(1+0.13)^-25÷0.13)} =$1,612,596.70

Difference= $1,488,071.1

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