A $76,000 trust is to be invested in bonds paying 8%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment must equal the mortgage investment. To earn a $6670 annual income from the investments, how much should the bank invest in bonds?
A) $21,000
B) $38,000
C) $17,000
D) $19,000
8 b + 7 c + 10 m = 667000
b + c + m = 76000
b + c = m = 38000
8 b + 7 c = 667000 - 10 m = 667000 - 380000 = 287000
7 b + 7 c = 7 * 38000 = 266000
subtracting equations ... b = 287000 - 266000
To solve this problem, we need to set up some equations based on the given information.
Let's assume the amount invested in bonds is B dollars.
Since the bond and CD investment must equal the mortgage investment, the amount invested in CDs is also B dollars.
The amount invested in mortgages would then be 2B dollars.
Now, let's calculate the income earned from each investment:
From the bond investment, the annual income would be (B * 0.08) dollars.
From the CD investment, the annual income would be (B * 0.07) dollars.
From the mortgage investment, the annual income would be (2B * 0.10) dollars.
The total income from all investments is $6670. So, we can set up the equation:
(B * 0.08) + (B * 0.07) + (2B * 0.10) = $6670
Simplifying the equation:
0.08B + 0.07B + 0.20B = $6670
0.35B = $6670
Dividing both sides of the equation by 0.35:
B = $6670 / 0.35
Calculating B:
B ≈ $19,057.14
Therefore, the bank should invest approximately $19,057.14 in bonds.
The answer choice that is closest to $19,057.14 is:
D) $19,000