You plan to invest $12,000 in two funds paying 41/2% and 5% simple interest. (There is more risk in the 5% fund.) Your goal is to obtain a total annual interest income of $580 from the investment. What is the smallest amount you can invest in the 5% fund and still meet your objective?
I dont know how to do it
To find out the smallest amount that can be invested in the 5% fund, we need to set up an equation based on the given information.
Let x be the amount invested in the 5% fund.
Since the total investment amount is $12,000, the amount invested in the 4.5% fund would be (12,000 - x).
Now, we can calculate the interest income from each investment:
Interest from the 5% fund = x * 0.05
Interest from the 4.5% fund = (12,000 - x) * 0.045
According to the problem, the total annual interest income should be $580, so we can set up the equation:
(x * 0.05) + ((12,000 - x) * 0.045) = 580
Now let's solve this equation to find the value of x.
0.05x + 0.045(12,000 - x) = 580
0.05x + 540 - 0.045x = 580
0.005x + 540 = 580
0.005x = 40
x = 40 / 0.005
x = 8,000
Therefore, the smallest amount that can be invested in the 5% fund while still meeting the objective is $8,000.