Suppose that you earn $50,000 annually.You expect expenses to drop by 22% for your family in the event of your death.Currently,if you die,you want to provide for your family for at least 15 more years,and the applicable after-tax and inflation return assumed is 5%.Using the earnings multiple approach provided in your textbook,what would be the amount of life insurance that you should purchase?

Question

Quizplus · Accepted Answer

First, we need to calculate the future expenses of the family.
Future expenses = Current expenses * (1- expected drop) = $50,000 * (1- 0.22) = $39,000

Next, we need to calculate the PV of future expenses for 15 years with a 5% after-tax and inflation return.
PV of future expenses = $39,000 * [(1- (1/1.05^15))/0.05] = $454,299

Then, we need to add the present value of the income that the family will lose due to the death.
Using the earnings multiple approach, we can assume that a reasonable multiple of the annual income is 8. So, the present value of the income that the family will lose is:
Present value of lost income = 8 * $50,000 * [(1-(1/1.05^15))/0.05] = $404,820

Finally, we add the present value of future expenses and present value of lost income to get the total amount of life insurance needed.
Total amount of life insurance = $454,299 + $404,820 = $859,119 ≈ $860,000

Therefore, the best choice is B, $404,820, as it is the closest option to the calculated amount.

Suppose That You Earn $50,000 Annually