Question

Country Day's scholarship fund receives a gift of $180000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75% interest, bonds pay 4.7% interest, and stocks pay 8.5% interest. Country day invests $ 45000 more in bonds than in CDs. If the annual income from the investments is $10570, how much was invested in each vehicle?

Country Day invested $ ___ in stocks.
Country Day invested $ ___ in bonds.
Country Day invested $ ___ in CDs.

Answer 1

By setting up equations based on the annual income from CDs, bonds, and stocks and solving for the investment amount in CDs, the amounts invested in each vehicle are $35,000 for CDs, $80,000 for bonds, and $65,000 for stocks.

Step-by-step explanation:

Let's denote the amount invested in CDs by C. According to the information given, the amount invested in bonds is C + $45,000. Because the total gift is $180,000, we can express the amount invested in stocks as $180,000 - C - (C + $45,000). Now, let's set up equations based on the annual income from each investment type:

• CDs: 0.0475C,
• Bonds: 0.047(C + $45,000),
• Stocks: 0.085($180,000 - 2C - $45,000).

The total annual income from all investments is $10,570. Hence, we can write the equation:

0.0475C + 0.047(C + $45,000) + 0.085($180,000 - 2C - $45,000) = $10,570.

Solving for C, and consequently for the amounts in bonds and stocks, gives us:

• CDs: $35,000,
• Bonds: $80,000 ($35,000 + $45,000),
• Stocks: $65,000 ($180,000 - $35,000 - $80,000).