question archive A brilliant young scientist is killed in a plane crash
A brilliant young scientist is killed in a plane crash
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A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $370,000 a year for the next 40 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 11 percent.
What is the difference between the present value of the settlement at 5 percent and 11 percent? Compute each one separately.
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The difference is $3036973.15.
Step-by-step explanation
This is an ordinary annuity.
The present value formula for an annuity is as follows;
Present value=payment*(1-(1+r)-n/r)
We are given the following data;
Payment=$370,000
Interest rates(r)=5%,11%
Number of periods(n)=40 years
Discount rate of 5%
Present value=370000*(1-(1.05)-40/0.05)
=370000*17.15908635
=$6348861.95
Discount rate of 11%
Present value=370000*(1-(1.11)-40/0.11)
=370000*8.951050817
=$3311888.802
The difference is as follows;
$6348861.95-$3311888.80
=$3036973.15
The difference between the two discount rates is $3036973.15.
