A $136000 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 $12040 annual income from the investments, how much should the bank invest in bonds?
Let x = amount in bonds
Then 68000-x is the amount in CDs
Now just add up the interest:
.08x + .07(68000-x) + .10*68000 = 12040
To find out how much the bank should invest in bonds, we need to set up an equation based on the given information.
Let's assume the amount invested in bonds, CDs, and mortgages is 'x'.
Since the bond and CD investment must equal the mortgage investment, we can say:
Amount invested in bonds = Amount invested in CDs = Amount invested in mortgages = x
The annual income earned from the bond investment will be 8% of the amount invested in bonds, i.e., 0.08x.
The annual income earned from the CD investment will be 7% of the amount invested in CDs, i.e., 0.07x.
The annual income earned from the mortgage investment will be 10% of the amount invested in mortgages, i.e., 0.10x.
Since the total annual income from all investments is $12,040, we can set up the equation:
0.08x + 0.07x + 0.10x = $12,040
Combining like terms, we get:
0.25x = $12,040
To solve for x, divide both sides of the equation by 0.25:
x = $12,040 / 0.25
x = $48,160
Therefore, the bank should invest $48,160 in bonds to earn a $12,040 annual income from the investments.