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Maricopa's Success scholarship fund receives a gift of $ 150000. The money is invested in stocks, bonds, and CDs. CDs pay 6 % interest, bonds pay 2.2 % interest, and stocks pay 11.7 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 10805 , how much was invested in each account?


Maricopa Success invested _____ in stocks.

Maricopa Success invested _____ in bonds.

Maricopa Success invested _____ in CDs.

Respuesta :

Answer:

$65,000 , $50,000 and $35,000

Step-by-step explanation:

Lets us assume the CDs be C, stocks be S and Bonds be B

Given that

Total scholarship fund received = $150,000

i.e

C + S + B = $150,000 ......................... (1)

Now the each items invested percentage is given

And, the annual income from investment is $10,805

So, the next equation is

0.06C + 0.022B + 0.117S = $10,805 ....................... (2)

And, it is mentioned that

The $15,000 more in bonds than in CDs

B = C + $15,000 ........................ (3)

Now put the equation 3 in equation C is

2C + S = $135,000  ........................... (4)

0.082C + 0.117S = $10,475 ........................... (5)

Now multiply the 0.117S in equation 4

So

0.234C + 0.117S = $15,795

0.082C + 0.117S = $10,475

After solving this

0.152C = $5,320

C = CDS = $35,000

So

B = $35,000 + $15,000

B=   Bonds = $50,000

And S = Stock = $65,000

Answer:

CDs = 35000, Bonds = 50000, Stock = 65000

Step-by-step explanation:

Let amount invested in : CDs be 'C' , stock be 'S' , bonds be 'B'

As per total funds : C + B + S = 150000 [E1]

As per interest rates : 0.06C + 0.022B + 0.117S = 10805 [E2]

Given (15000 more invested in bonds than CDs :  B = C + 15000 [E3]

Putting equations : [E3] in [E2] & [E1]

C + (C+15000) + S = 150000 → 2C + 15000 + S = 150000

  • 2C + S = 135000 [E4]

0.06C+0.022(C+15000)+0.117S = 10805 → 0.06C+0.022C+330+0.117S = 10805

  • 0.082C + 0.117S + 330 = 10805 → 0.082C + 0.117S = 10475 [E5]

By putting value of S from [E4] in [E5] :

0.082C + 0.117 (135000 - 2C) = 10475 → 0.082C + 15795 - 0.234C = 10475

5320 = 0.152C  → C = 5320 / 0.152 = 35000 [CDs]

B = C + 15000 = 35000 + 15000 = 50000 [Bonds]

By [E1]: 35000+50000+S = 150000 → S = 150000 - 85000 = 65000 [Stocks]

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