Invested amount = $27,000
Interest is getting 7% on $27,000 of bonds.
Let us assume additional money should invest = $x.
Interest payed on additional money invested = 4%.
Total money invested = 27,000 + x.
Total interest on both amount should be equal to = 6%.
We can setup an equation as
7% of starting invested amount + 4% of additional invested amount = 6% of total invested amount.
0.07 * 27,000 + 0.04 x = 0.06(27,000+x).
On simplifying, we get
1890 +0.04x = 0.06(27000+x).
Distributing 0.06 over (27000+x), we get
1890 +0.04x = 1620 +0.06x
Subtracting 0.04x from both sides, we get
1890 +0.04x-0.04x = 1620 +0.06x - 0.04x
1890 = 1620 + 0.02x
Subtracting 1620 on both sides
1890 -1620 = 1620 -1620 + 0.02x.
270 = 0.02x.
Dividing both sides by 0.02, we get
270/0.02 = 0.02x/0.02
13500 = x.
Therefore, $13500 is the additional money should they invest.