Erin invests $3750 spread across three funds; Fund A, Fund B, and Fund C. Over t

Question

Erin invests $3750 spread across three funds; Fund A, Fund B, and Fund C. Over the course of the following year,

Fund A earned a 3% return, Fund B earned a 8% return, and Fund C earned a 9% return. The annual return for Fund

A(in dollars) was equal to %20 of the total return from all three funds fir the year. The amount invested in Fund B was equal to 1.2 times the amount invested in Fund C.

a) Set up a system of equations that you can use to find the amounts invested in each of the three funds. Clearly indicate what any variables in your system represent.

b) Solve the system you set up in Part (a) using the rref calculator function. State your answer, along with a short explanation of what each of the numbers mean.

Explanation / Answer

Assuming that Amount invested in Fund A X Amount invested in Fund B Y Amount invested in Fund C Z X + Y + Z = 3,750 $ Return (Fundwise) Fund A 3%* X Fund B 8%* Y Fund C 9%* Z 3% of X = 20% of (3% * X + 8% * Y + 9% * Z) Therefore, 0.03 X = .2 (0.03 X + 0.08 Y + 0.09 Z) Further, Y = 1.2 Z (investment in Fund B is 1.2 times the amount invested in Fund C) Hence, 0.03 X = .2 (.03 X + .096 Z + .09 Z) Therefore, .03 X = 0.006X + 0.186Z Hence, 0.294 X = .0186 Z X = 0.186 Z / 0.294 0.632653 X = 0.63 Z Total amount invested = $ 3,750 Combining the individual values represented as a part of Z .63 Z + 1.2 Z + Z = 3,750 $ Hence, Z=         1,325 $ Y = 1.2 * Z         1,590 $ X = 0.63 * Z            835 $

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