Question

Green River Community College scholarship fund receives a gift of $ 160000. The money is invested in stocks, bonds, and CDs. CDs pay 2 % interest, bonds pay 2.8 % interest, and stocks pay 9.8 % interest. GRCC invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 7580 , how much was invested in each vehicle?

Answer 1

$50,000 Stocks; $60,000 Bonds; and $50,000 CDs

Step-by-step explanation:

We will establish a series of equations from the question.

Equation 1. The $160,000 gift is invested in stocks, bonds and CDs.

Thus Stock Investment (S) + Bond Inv. (B) + CDs Inv. (C) = $160,000 (Equation 1)

Equation 2. GRCC invests $10,000 more in bonds than in CDs. Thus we can say

Bond Investment (B) = CDs Inv. (C) + 10,000. (Equation 2)

Accordingly, we transform equation 1 as follows.

S + (C + 10,000) + C = 160,000 (Equation 3)

We can deduce an Equation 4 for S from Equation 3, as follows.

S + (C + 10,000) + C = 160,000

= S + 2C + 10,000 = 160,000

= S = 160,000 - 10,000 - 2C

= S = 150,000 - 2C (Equation 4)

With an interest rate of 2% on CDs, 2.8% on bonds, and 9.8% in stocks, total income = $7,580.

Thus, (2%*C) + (2.8%*B) + (9.8%*S) = 7,580

= (0.02*C) + (0.028 * (C+10,000)) + (0.098*(150,000-2C)) = 7,580

= 0.02C + 0.028C + 280 + 14,700 - 0.196C = 7,580

= 14,980 - 0.148C = 7,580

= 14,980 - 7,580 = 0.148C

= 7,400 = 0.148C

= C = CD Investment = (7,400/0.148) = 50,000.

Using Equation 4, we get the investment in stock as follows.

S = 150,000 - 2C (Equation 3)

= 150,000 - 2(50,000)

= 150,000 - 100,000

= S = Stock Investment = 50,000.

Using Equation 2, we get the investment in bonds as follows.

Bond Investment (B) = CDs Inv. (C) + 10,000. (Equation 2)

= B = C + 10,000

= 50,000 + 10,000

= B = Bond Investment = 60,000.