Question

An investor has $300,000 to invest, part at 12% and the remainder in a less risky investment at

7%. If her investment goal is to have an annual income of $27,000, how much should she put in
each investment?

Answer 1

$120,000 at 12% and $180,000 at 7%

Explanation:

The annual income is the simple interest to be received in a year from the two investments. The simple interest I from a principal amount P invested at a rate R for a time period T may be given as

I = PRT/100

As such, let the principal amount invested in and the interest from the first investment be Y and a respectively. If the investor has $300,000 to invest, it means that the amount invested in the less risky investment will be $300,000 - Y

Given that the annual income is $27,000, then

a = Y * 12/100

a = 0.12 Y

and

27000 - a = (300,000 - Y) * 7 / 100

2,700,000 - 100a = 2,100,000 - 7Y

600,000 = 100a - 7Y

600,000 = 12Y - 7Y

5Y = 600,000

Y = 120,000

300000 - Y

= 300,000 - 120,000

= 180,000