Question

Part 4:

1. A woman has been injured in an automobile accident and as a result is permanently disabled for life. (The accident was not her fault.) She is 35 years of age and had planned on working until age 70. As a potential college professor, she was about to start a job that paid $50,000 annually. Using 6%, what is the amount of lost income in present-day dollars?

2. Additionally, she faces annual medical bills of $30,000, all of which are related to the accident. Her life expectancy is age 85. Using 6%, what is the amount of the medical expenses in present-day dollars?

3. Also, during retirement she had planned on receiving $75,000 per year. What is the present-day value of the lost pension? Note: This part requires two calculations.

4. How much should she sue for in court in terms of damages and lost compensation ? Ignore attorney fees?

Answer 1

The question is a present value annuity problems with the facts given herewith:

Interest rate = 6% in all cases

Retirement age = 70 years

1. Expected Annual income = $ 50,000

No of years of employment = 70 - 35 = 35 years

Rate of interest = 6%

So, Present value = PMT * [1 - { 1 / (1 + R)ⁿ} / R]

or, Present value = 50,000 * [1 - { 1 / (1 + 6%)³⁵} / 0.06]

Hence the Amount of lost income in Present day = $ 6,405,072

2. Annual medical expense = $ 30,000

No. of years of payment = 85 - 35 = 50 years

Rate of Interest = 6%

So, the Present value = PMT * [1 - { 1 / (1 + R)ⁿ} / R]

or, Present value = 30,000 * [1 - { 1 / (1 + 6%)⁵⁰} / 0.06]

Hence the Amount of the medical expenses in present day = $ 9,210,077

3. This question has two parts (a). we have to calculate the future value of retirement amount of $ 75,000 received for a span of 15 (85 -70) years, and (b). we have to calculate the same value in the present day.

a. Future value = PMT * [ { (1 + R)ⁿ - 1 } / R]

or, FV = 75,000 * [ { (1 + 6%)¹⁵ - 1 } / 0.06]

So, Future value of the retirement for 15 years = $ 1,745,698

Hence the present value of the future amount = Future value / [ 1 + R%]ⁿ

= 1,745,698 / (1.06)⁵⁰

= $ 94,771

4. Total Amount she should sue for in terms of damages and lost compensation = the Sum of the value calculated in part 1, 2 and 3 =  6,405,072 + 9,210,077 + 94,771

= $ 15,615,149

Hope this has solves the query.