A trust fund has $200,000 to invest. Three alternative investments have been identified, earning 10 percent, 7 percent, and 8 percent, respectively. A

preprekomW

preprekomW

Answered question

2021-06-13

A trust fund has $200,000 to invest. Three alternative investments have been identified, earning 10 percent, 7 percent, and 8 percent, respectively. A goal has been set to earn an annual income of $16,000 on the total investment. One condition set by the trust is that the combined investment in alternatives 2 and 3 should be triple the amount invested in alternative 1. Determine the amount of money which should be invested in each option to satisfy the requirements of the trust fund.

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-06-15Added 169 answers

Ian Adams

Ian Adams

Skilled2021-08-04Added 163 answers

Let x be the amount invested at 10%, yy be the amount invested at 7%, and z be the amount invested at 8%.
The total investment is $200000:
x+y+z=200000(1)
The annual income is $16,000:
0.10x+0.07y+0.08z=16000(2)
The combined investment in alternatives 2 and 3 should be triple the amount invested in alternative 1 so:
y+z=3x
or
3x+y+z=03x+y+z=0tag{3}$$
Subtract each side of (1) and (3) then solve for xx:
4x=200000
x=50000
Substitute x=50000 to (2) and simplify to obtain (4):
0.10(50000)+0.07y+0.08z=16000
5000+0.07y+0.08z=16000
0.07y+0.08z=11000(4)
Substitute x=50000 to (1) and simplify to obtain (5):
50000+y+z=200000
y+z=150000(5)
Eliminate zz. Multiply (5) by 0.08 to obtain (6):
0.08y+0.08z=12000(6)
Subtract each side of (4) and (5) then solve for x:
0.01y=1000
y=100000
Solve for zz using (5):
100000+z=150000
z=50000
So, $50000 was invested at 10%, $100000 was invested at 7%, and $50000 was invested at 8%.

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