A total of $80,000 is invested in two funds paying 2.3% and 3.1% simple interest . The total annual interest is $2000. How much is invested in each fund?
To solve this problem, we can use a system of equations.
Let's say the amount invested in the first fund, paying 2.3% interest, is x dollars. Then, the amount invested in the second fund, paying 3.1% interest, would be (80000 - x) dollars because the total investment is $80,000.
Now, for each fund, we can calculate the amount of interest earned using the simple interest formula: Interest = Principal x Rate.
For the first fund, the interest earned would be (x)(0.023), as the interest rate is 2.3%. Similarly, for the second fund, the interest earned would be ((80000 - x)(0.031)).
According to the problem, the total annual interest is $2000. Hence, we can set up the equation:
(x)(0.023) + ((80000 - x)(0.031)) = 2000
Let's solve this equation step by step:
0.023x + 2480 - 0.031x = 2000
-0.008x + 2480 = 2000
-0.008x = -480
x = 60000
So, $60,000 is invested in the first fund (2.3% interest), and the remainder, $20,000, is invested in the second fund (3.1% interest).
If $x is invested at 2.3%, the rest (80000-x) is at 3.1%
So, adding up the interest, we get
.023x + .031(80000-x) = 2000