An inheritance of $50,000 is divided into two investments earning 8.5% and 10% simple interest. ( The 10% investment has a greater risk.) Your objective is to obtain a total annual interest income of $4700 form the investments. What is the smallest amount you can invest at 10% in order to meet your objective?
A = amt invested at 8.5%
B = amt invested at 10%
A + B = 50000 or
A = 50000 - B
income = 0.085A + 0.10B = 4700
substitute A in terms of B and solve
a = nothing
To find the smallest amount that should be invested at a 10% interest rate, we need to set up an equation based on the given information.
Let's say x represents the amount invested at a 10% interest rate. Therefore, the amount invested at 8.5% would be $50,000 - x (since the total inheritance is $50,000).
Now, let's calculate the interest earned from each investment:
Interest from the 10% investment: 0.10x
Interest from the 8.5% investment: 0.085($50,000 - x)
According to the problem, the total annual interest income needs to be $4700. Therefore, we set up this equation:
0.10x + 0.085($50,000 - x) = $4700
Now, let's solve this equation to find the value of x (the amount invested at 10%):
0.10x + 0.085($50,000 - x) = $4700
0.10x + 0.085($50,000) - 0.085(x) = $4700
0.10x + $4250 - 0.085x = $4700
0.015x + $4250 = $4700
0.015x = $450
x = $450 / 0.015
x ≈ $30,000
Therefore, the minimum amount that should be invested at a 10% interest rate to meet the objective of earning a total annual interest income of $4700 is approximately $30,000.