Becky has saved $4500. She would like to earn $325 per year, by investing into two different investments: a low-risk investment that pays 5% annual interest and a high -risk investment that pays 9% annual interest.
How much should Becky invest in each type of investment?
To determine how much Becky should invest in each type of investment, we can use a system of equations.
Let's assume Becky invests x dollars in the low-risk investment and y dollars in the high-risk investment.
From the given information, we can set up the following equations:
Equation 1: The total amount invested is $4500.
x + y = 4500
Equation 2: The total annual interest earned should be $325.
0.05x + 0.09y = 325
Now, we can solve this system of equations using either substitution or elimination method.
Let's solve it using the elimination method:
Multiply both sides of Equation 1 by 0.05:
0.05x + 0.05y = 0.05 * 4500
0.05x + 0.09y = 325
Subtract Equation 2 from Equation 1:
(0.05x + 0.05y) - (0.05x + 0.09y) = 225 - 325
0.05y - 0.09y = -100
-0.04y = -100
Divide both sides by -0.04:
y = (-100) / (-0.04)
y = 2500
Now substitute the value of y back into Equation 1 to solve for x:
x + 2500 = 4500
x = 4500 - 2500
x = 2000
Therefore, Becky should invest $2000 in the low-risk investment (5% interest) and $2500 in the high-risk investment (9% interest) to earn a total of $325 per year.