annual income vs investments

Question

Edmonds Community College's (EDCC) scholarship fund received a gift of $ 300,000. 

The money is invested in stocks, bonds, and CDs.

CDs pay 3% interest, bonds pay 3.4% interest, and stocks pay 7.1% simple interest.

To better secure the total investment EDCC invests 3 times more in CDs than the sum of the stocks and bonds investments

If the annual income from the investments is $10,225 , how much was invested in each vehicle? 

solve by the method of your choice either using reduced row echelon form or the matrix equation

EDCC invested

$ in stocks

$ in bonds

$ in CDs

Answer 1

Let CD= CD investment, S = Stock investment and B = Bond investment

Set up first equation representing interest income. 0.03CD + 0.034B + 0.071S = $10,225.00

Then recognize that the second equation comes from the CD investment equal to three times the sum of other two investments (bonds and stocks). (If CD=3(B+S), so CD-3(B+S) =0)

Then, set up third equation representing investment totals: CD + B + S = $300,000.00.

You can see the matrix below based on the coefficients in each of the three equations:

0.03 0.034 0.071 | 10,225

1 -3 -3 | 0

1 1 1 | 300,000

I then used substitution 4/3CD = 300,000 and B = 75,000 - S to solve for all three investment amounts.

However, you could also use the elimination (addition) method to find this answer set.

Another method to find this answer set, which is beyond the scope of this message, is to use Cramer's Rule.

Answer:

CD = $225,000

B = $50,000

S = $25,000

Please contact me for more tutoring.

Thank you.

Ira S.