A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,300, and risk factors make it prudent to invest some money in all three investments. Let x denote the amount invested at 8 %, y denote the amount invested at 7%, and z denote the amount invested at 10%. Find a general description for the amounts invested at the three rates.
A) , with
B) , with
C) , with
D) , with
E) , with

Question

A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,300, and risk factors make it prudent to invest some money in all three investments. Let x denote the amount invested at 8 %, y denote the amount invested at 7%, and z denote the amount invested at 10%. Find a general description for the amounts invested at the three rates. ​
A) , with 
B) , with 
C) , with 
D) , with 
E) , with

Quizplus · Accepted Answer

We can use a system of equations to solve for the amounts invested at each rate. Let x, y, and z be the amounts invested at 8%, 7%, and 10%, respectively. Then we have the following system of equations:

x + y + z = 220,000 (total amount invested)
0.08x + 0.07y + 0.1z = 16,300 (total interest earned)

We can solve this system using Gaussian elimination or a similar method. The solution is:

x = $42,000 invested at 8%
y = $88,000 invested at 7%
z = $90,000 invested at 10%

Therefore, the best choice is B, which matches these values.

A Trust Account Manager Has $220,000 to Be Invested