Question

Country Day's scholarship fund receives a gift of$150000. The money is invested in stocks, bonds, and CDs. CDs pay 5.4% interest, bonds pay 6% interest, and stocks pay 7.7% interest. Country day invests $50000 more in bonds than in CDs. If the annual income from the investments is $9700, how much was invested in each vehicle?

$ _ on CD’s.
$ _ on stocks.
$ _ on bonds.

Answer 1

The $21,591.27 was invested in CDs, $67,954.92 was invested in stocks, and $60,453.81 was invested in bonds.

Step-by-step explanation:

Let's denote the amount invested in CDs as C, the amount invested in stocks as S, and the amount invested in bonds as B.

According to the given information, we have the following three equations:

1. C + S + B = $150,000
2. S = 0.077S
3. B = C + $50,000

We also know that the annual income from the investments is $9,700, which can be expressed as:

0.054C + 0.077S + 0.06B = $9,700

Now, we can solve this system of equations to find the amounts invested in each vehicle.

1. Substituting the second equation into the third equation, we get B = 0.077S + $50,000
2. Substituting the third equation into the first equation, we get C + S + (0.077S + $50,000) = $150,000
3. Combining like terms, we have C + 1.154S = $100,000
4. Substituting C + 1.154S = $100,000 in the annual income equation, we get 0.054C + 0.077S + 0.06(0.077S + $50,000) = $9,700
5. Simplifying the equation, we have 0.054C + 0.077S + 0.00462S + $3,000 = $9,700
6. Combining like terms, we get 0.054C + 0.08162S = $6,700
7. Substituting C + 1.154S = $100,000 in the equation, we have 0.054(100,000 - 1.154S) + 0.08162S = $6,700
8. Expanding and simplifying the equation, we get 5,400 - 0.062496S + 0.08162S = $6,700
9. Combining like terms, we have 0.019124S = $1,300
10. Dividing both sides by 0.019124, we get S = $67,954.92
11. Substituting S = $67,954.92 in C + 1.154S = $100,000, we get C + 1.154($67,954.92) = $100,000
12. Simplifying the equation, we have C + $78,408.73 = $100,000
13. Subtracting $78,408.73 from both sides, we get C = $21,591.27
14. Finally, substituting the values of C and S back into the first equation, we have $21,591.27 + $67,954.92 + B = $150,000
15. Simplifying the equation, we have B = $60,453.81

Therefore, the amounts invested in each vehicle are:

• $21,591.27 on CDs
• $67,954.92 on stocks
• $60,453.81 on bonds