A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $350,000 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 8 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 12 percent.

What is the difference between the present value of the settlement at 8 percent and 12 percent? Compute each one separately.

To calculate the difference in the present value of the settlement at discount rates of 8% and 12%, we'll use the formula for the **present value of an annuity**. The formula is:

\[
PV = P \times \frac{1 - (1 + r)^{-n}}{r}
\]

Where:
- $PV$ is the present value of the annuity (settlement),
- $P$ is the annual payment ($350,000),
- $r$ is the discount rate (either 8% or 12%),
- $n$ is the number of years (25 years).

### Step 1: Present Value at 8%
Using the formula for an 8% discount rate ($r = 0.08$):

\[
PV_{8\%} = 350,000 \times \frac{1 - (1 + 0.08)^{-25}}{0.08}
\]

### Step 2: Present Value at 12%
Similarly, for a 12% discount rate ($r = 0.12$):

\[
PV_{12\%} = 350,000 \times \frac{1 - (1 + 0.12)^{-25}}{0.12}
\]

### Step 3: Difference
After calculating the present values, the difference between the settlement at 8% and 12% will be:

\[
\text{Difference} = PV_{8\%} - PV_{12\%}
\]

Let me compute this.The present value of the settlement is:

- **At 8% discount rate**: \$3,736,171.67
- **At 12% discount rate**: \$2,745,098.69

The difference between the two present values is \$991,072.98.

Would you like more details or have any questions?

Here are some related questions:
1. How does the discount rate impact long-term financial projections?
2. What factors should be considered when choosing a discount rate in legal settlements?
3. How would the calculation change if the income stream were not constant over 25 years?
4. How would inflation affect the future value of these settlements?
5. What are the implications of using a different time period, like 30 or 40 years?

**Tip:** Always check if future earnings estimates are adjusted for inflation when calculating present value!

A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $350,000 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 8 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 12 percent. What is the difference between the present value of the settlement at 8 percent and 12 percent? Compute each one separately.

Learn how to compute the difference in the present value of a $350,000 annual income over 25 years, discounted at 8% and 12%. This problem involves present value of annuities and time value of money concepts, suitable for advanced high school or college students.

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