Question

Kyle inherited $26 000 and invested part of it in a money market account, part in municipal bonds and rest in a mutual fund. After one year, he received a total of $1265 in simple interest from the three investments. The money market paid 4% annually, the bonds paid 5% annually, and the mutual funds paid 8% annually. There was $5 000 more invested in the bonds than the mutual funds. Find the amount Kyle invested in each category.

Answer 1

To find the amounts Kyle invested in each category with his $26,000 inheritance, we set up a system of equations based on the given interest rates and total interest received after one year. By solving these equations, we determine how much was invested in the money market account, municipal bonds, and mutual fund.

Step-by-step explanation:

Kyle needs to divide his $26,000 inheritance among three different types of investments: a money market account, municipal bonds, and a mutual fund. The investments have varying interest rates: 4% for the money market, 5% for the bonds, and 8% for the mutual fund. It was also given that there was $5,000 more invested in bonds than in the mutual funds. To find the amount Kyle invested in each category, we need to set up a system of equations.

Let x represent the amount invested in the mutual fund, x + $5,000 represent the amount invested in bonds, and $26,000 - x - (x + $5,000) represent the amount invested in the money market. Now, the total interest from all investments after one year was $1,265, which gives us the equation: 0.04(26,000 - 2x - 5,000) + 0.05(x + 5,000) + 0.08x = 1,265. By solving this equation, we can find the amount Kyle invested in each category.