Answer:
John invested $2,000 in money-market fund, $3,000 in municipal bonds, and $7,000 in mutual funds.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
John invested his inheritance of $12,000 in three different funds: part in a money-market fund paying 3% interest annually; part in municipal bonds paying 4% annually; and the rest in mutual funds paying 7% annually. John invested $4,000 more in mutual funds than he invested in municipal bonds. The total interest earned in one year was $670. How much did he invest in each type of fund?
The explanation of the answer is now given as follows:
Let a, b and c represent the amount invested in money-market fund, municipal bonds and mutual funds respectively. Therefore, the sum of the three principal amounts can be represented as follows:
a + b + c = 12,000 ……………………….. (1)
Since John invested $4,000 more in mutual funds than he invested in municipal bonds, we have:
c = b + 4,000 ……………………………. (2)
The total amount of interest earned from each fund can be represented as follows:
0.03a + 0.04b + 0.07c = 670 ………………. (3)
Substituting equation (2) into equation (1), we have:
a + b + b + 4,000 = 12,000
a + 2b = 12,000 – 4,000
a + 2b = 8,000
a = 8,000 – 2b ……………………….. (4)
Also, substituting equation (2) into equation (3), we have:
0.03a + 0.04b + 0.07(b + 4,000) = 670
0.03a + 0.04b + 0.07b + 280 = 670
0.03a + 0.04b + 0.07b 0 = 670 – 280
0.03a + 0.11b = 390 ,,,,,,,,,,,,,,,,,,,,,, (5)
Substituting equation (4) into equation (5) and solve for b, we have:
0.03(8,000 – 2b) + 0.11b = 390
240 – 0.06b + 0.11b = 390
240 + 0.05b = 390
0.05b = 390 – 240
0.05b = 150
b = 150 / 0.05
b = 3,000
Substituting b = 3,000 into equation (2), we have:
c = 3,000 + 4,000
c = 7,000
Also, substituting b = 3,000 into equation (4), we have:
a = 8,000 – (2 * 3,000)
a = 8,000 – 6,000
a = 2,000
Therefore, John invested $2,000 in money-market fund, $3,000 in municipal bonds, and $7,000 in mutual funds.
Subtract 6 from both sides to solve.