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 [tex]5.75 \%[/tex]
[tex]\Rightarrow \text{Interest from CDs} = x \times \dfrac{5.75}{100} ...... (1)[/tex]
As per question, amount invested in bonds is $(x+30000).
Interest received from bonds is [tex]5.8 \%[/tex].
[tex]\Rightarrow \text{Interest from bonds} = (x+30000) \times \dfrac{5.8}{100} ...... (2)[/tex]
Total amount is $115000.
So, amount invested in stocks = Total amount - Amount invested in CDs and Bonds
[tex]\Rightarrow 115000 - x - (x+30000)\\ \Rightarrow (85000-2x)[/tex]
Interest received from stocks is [tex]6.4 \%[/tex] [tex]\Rightarrow \text{Interest from Stocks} = (85000-2x) \times \dfrac{6.4}{100} ...... (3)[/tex]
Total annual income from interest is $6930.
Adding equations (1), (2) and (3) and putting it equal to 6930.
[tex]\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[/tex]
Amount invested in CDs is $20000.
Amount invested in Bonds is (x + 30000)= $20000+$30000 = $50000.
Amount invested in Stocks is [tex]\(85000 - 2 \times x\) = \(85000 - 2 \times 20000\)[/tex]= $45000.
