Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.
We follow these steps in order to arrive at the answer:
Let the amount invested in bonds be x
Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.
The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x
The interest earned on bonds will be 0.06x0.06x
The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x
The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x
The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.
Hence total interest is:
1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x
Simplifying we get,
1000 -400 = 0.1x1000−400=0.1x
600 = 0.1x600=0.1x
\mathbf{x = 6,000}x=6,000
Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000
Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000