Answer:
In order to obtain a return of 9% per year, we need to invest $133,333.333 in low risk investments, $0 in mid risk investment and $66,666.666 in high risk investment.
Step-by-step explanation:
2/3 of the $200,000 for investment should go to low risk, and the other third to mid risk and high risk. Lets call X the amount that goes into high risk, then the amount that goes to mid risk is 200,000/3 - X.
If we want a 9% of return for the total investment, then we should end with $200,000 * 1.09 = $218,000. We can compute what money we expect to end the year with in terms of X and then obtain the value of X.
We end the year with
200,000 * 1.06 * 2/3 + (200,000/3 - X) * 1.09 + X * 1.15 = 214000 + X * (1.15 - 1.09) = 214000 + X * 0.06
Since we want this amount to be equal to 218000, then
214000+X * 0.06 = 218000
X*0.06 = 218000-214000 = 4000
X = 4000/0.06 = 66,666.666 = 200,000/3
Thus, we are not investing in the mid risk category.
In order to obtain a return of 9% per year, we need to invest $200,000/3 = $133,333.333 in low risk investments, $0 in mid risk investment and $66,666.666 in high risk investment.
