Question

Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks, bonds, and CDs. CDs pay 5.75 % interest, bonds pay 5.8 % interest, and stocks pay 6.4 % interest. Maricopa Success invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 6930 , how much was invested in each account?

Answer 1

Answer:

Amount invested in CDs is $20000.

Amount invested in Bonds is $50000.

Amount invested in Stocks is $45000.

Step-by-step explanation:

Let amount invested in CDs be $x.

Interest received from CDs is $5.75 \%$

$\Rightarrow \text{Interest from CDs} = x \times \dfrac{5.75}{100} ...... (1)$

As per question, amount invested in bonds is $(x+30000).

Interest received from bonds is $5.8 \%$.

$\Rightarrow \text{Interest from bonds} = (x+30000) \times \dfrac{5.8}{100} ...... (2)$

Total amount is $115000.

So, amount invested in stocks = Total amount - Amount invested in CDs and Bonds

$\Rightarrow 115000 - x - (x+30000)\\ \Rightarrow (85000-2x)$

Interest received from stocks is $6.4 \%$ $\Rightarrow \text{Interest from Stocks} = (85000-2x) \times \dfrac{6.4}{100} ...... (3)$

Total annual income from interest is $6930.

Adding equations (1), (2) and (3) and putting it equal to 6930.

$\Rightarrow x \times \dfrac{5.75}{100} + (x+30000) \times \dfrac{5.8}{100} + (85000-2x) \times \dfrac{6.4}{100} = 6930\\\Rightarrow (12.8x - 11.55x) = 544000 + 174000 - 693000\\\Rightarrow 1.25x = 25000\\\Rightarrow x = 20000$

Amount invested in CDs is $20000.

Amount invested in Bonds is (x + 30000)= $20000+$30000 = $50000.

Amount invested in Stocks is $\(85000 - 2 \times x\) = \(85000 - 2 \times 20000\)$= $45000.