Question

The court ruled that Lox Auto was liable in the death of an employee.The settlement called for the company to pay the employee's widow $60,000 at theend of each year for 20 years. Find the amount the company must set aside today,assuming 5% compounded annually.

Answer 1

We have to calculate the present value PV of a annuity.

The payment is yearly and it is P=60,000.

The interest rate is 5% (r=0.05), compounded annually (m=1).

The number of periods is n=20 years.

Then, we can use the formula for the present value of a annuity:

`\begin{gathered} PV=P\cdot(1-(1)/((1+r)^n))/(r) \\ PV=60000\cdot(1-(1)/(1.05^(20)))/(0.05) \\ PV\approx60000\cdot(1-(1)/(2.653))/(0.05) \\ PV\approx60000\cdot(1-0.377)/(0.05) \\ PV\approx60000\cdot(0.623)/(0.05) \\ PV\approx60000\cdot12.462 \\ PV\approx747720 \end{gathered}`

Answer: the company must set aside $747,720.