A $148,000 trust is to be invested in bonds paying 7%, CDs paying 6%, and mortgages paying 8%. The bond and CD investment must equal the mortgage investment. To earn a $10,860 annual income from the investments, how much should the bank invest in bonds?
To solve this problem, we need to analyze the given information step by step.
Let's assume the amount invested in bonds, CDs, and mortgages is x dollars each. Since the bond and CD investment must equal the mortgage investment, we can say:
Investment in Bonds + Investment in CDs = Investment in Mortgages
Now, let's calculate the annual income generated from each investment:
Income from Bonds = Investment in Bonds × Interest Rate for Bonds (7%)
Income from CDs = Investment in CDs × Interest Rate for CDs (6%)
Income from Mortgages = Investment in Mortgages × Interest Rate for Mortgages (8%)
Given that the total annual income from the investments is $10,860, we can write the equation:
Income from Bonds + Income from CDs + Income from Mortgages = $10,860
Now, let's substitute the values in the equations and solve them.
Income from Bonds = x × 7/100 = 0.07x
Income from CDs = x × 6/100 = 0.06x
Income from Mortgages = x × 8/100 = 0.08x
By substituting the values into the equation, we get:
0.07x + 0.06x + 0.08x = $10,860
Combining like terms, we have:
0.21x = $10,860
To find the value of x, we need to divide both sides of the equation by 0.21:
x = $10,860 ÷ 0.21
x ≈ $51,714.29
Therefore, the bank should invest approximately $51,714.29 in bonds to earn an annual income of $10,860.