Question

Westboro Industrial earned a $200,000 profit this year. The company needs to buy a new ventilation system at the end of year 7 at a cost of $75,000. The company also wants to invest in a new product line at the end of year 10 at an estimated cost of $100,000. Westboro would like to deposit the profit from this year to pay for these future expenses and then give the remainder of the money to the employees as a bonus. How much of the $200,000 can the company use for bonuses and still pay for the future expenses? Use a nominal annual interest rate of 6% compounded annually to make the calculations

Answer 1

This is a simple problem. We need to fina a sum x such that a portion of it, say y, becomes equal to 75,000 at the end of year 7 at 6% compounded annually. And the balance, say x-y, becomes equal to 100,000 at the end of year 10 at 6% compounded annually.

So 75,000 = y * (1.06^7), so y = 75000 / 1.06^7 = 49,879

100,000 = (x-y) * (1.06^10), so x-y = 100,000 / 1.06^10 = 55,839

Hence x = 49,879 + 55,839 = 106,718

Since the profit this year is 200,000, teh balance, ie. 200000 - 106718 = 93,282 can be paid out as bonus.