Question

Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6.7 % interest, bonds pay 2.5 % interest, and CDs pay 5.75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977.5 , how much was invested in each account?

Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.

Answer 1

• stocks: $45000
• bonds: $55000
• CDs: $45000

Explanation:

You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.

Setup

We can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...

• s + b + c = 145000
• b - c = 10000
• 0.067s +0.025b +0.0575c = 6977.50

Solution

These equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.

We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...

• stocks: $45000
• bonds: $55000
• CDs: $45000

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Additional comment

Using b = c +10000, the two remaining equations are ...

• s +2c = 135000
• 0.067s +0.0825c = 6727.50

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