Question

John invested his inheritance of $12000 in 3 different funds part in a money market fund paying 3% interest annually Parton monusco bonds paying 4% annually and the rest in mutual funds paying 7% annually John invested 4000 more in mutual funds than he invested in municipal bonds the total interest in one year with $670

Answer 1

To solve this problem, we can set up an equation based on the interest earned from each fund and the total interest earned. By solving this equation, we can find the amounts invested in the money-market fund, municipal bonds, and mutual funds.

Let's assume the amount invested in the money-market fund is x dollars.

Since John invested $4,000 more in mutual funds than in municipal bonds, the amount invested in mutual funds would be (x + 4000) dollars.

The remaining amount invested in municipal bonds would be ((12,000 - x - (x + 4000)) = (12,000 - 2x - 4000) dollars.

The total interest earned in one year is the sum of the interest earned from each fund:

• Interest from money-market fund = (3/100) * x dollars
• Interest from municipal bonds = (4/100) * ((12,000 - 2x - 4000)) dollars
• Interest from mutual funds = (7/100) * (x + 4000) dollars

According to the given information, the total interest earned is $670.

So, we can set up the equation:

(3/100) * x + (4/100) * (12,000 - 2x - 4000) + (7/100) * (x + 4000) = 670

Solving this equation will give us the value of x, which represents the amount invested in the money-market fund.

By substituting this value back into the expressions for the amounts invested in municipal bonds and mutual funds, we can find the final investment amounts.

Question:

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?

Answer 2

John invested $2,000 in money-market fund, $3,000 in municipal bonds, and $7,000 in mutual funds.

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.