Lux Investing
a renowned mathematician recieved a 60,000 bonus to accept a tenured professorship at a university.?
she invested of the bonus in fixed income securities yielding 6% annually. The rest of the bonus money was invested in a high tech start up expecting to yield 30% annually to it's investors. How much was invested in tech business if she expected to earn 12240 annually from investments
Public Comments
- Let x be the amount invested at 6% Let y be the amount invested at 30% Then x+ y = 60,000 x * 0.06 + y * 0.30 = 12240. You now have two equations with two unknowns. You can solve by substitution, elimination or Cramer's Rule. I used the web site referenced below. x=24,000 y = 36,000 So the Professor invested $24k at 6% and $36K at 30%. (Then got into big trouble for not paying taxes on the bonus.)
- Charles's answer is better, in that it's a more general approach, but for many problems like this you can solve without an "extra" variable. Here, you want to know the amount invested in tech business (at 30% or .30 interest), so call that x. The remaining money is (60,000-x), and that is invested at 6% or .06 interest. The total annual earnings are: x*0.30 + (60,000-x)*0.06 = 12,240 which I have set equal to 12,240 since that is the desired annual return. Now, just simplify the left side. Use the distributive law to "multiply out" the messy term on the right, and then combine the two x terms: x*0.30 + 3,600 - x*0.06 = 12,440 x*0.36 + 3,600 = 12,440 Now, solve for x as a two-step equation. That gives the answer in just four simple steps.
