A total of $25,000 is invested in two funds paying 8% and 8.5% simple interest. The annual interest is $2040. How much is invested in each fund?

Question

A total of $25,000 is invested in two funds paying 8% and 8.5% simple interest. The annual interest is $2040. How much is invested in each fund?

Answer 1

This is a system of 2 linear equations problem. Because there are two unknowns (how much is invested in the first fund and how much is invested in the second fund) we need to create two equations.

 

1) Let's start by establishing our variables:

x is the amount invested in the first (the 8%) fund

y is the amount invested in the second (8.5%) fund

 

2) Then we need to come up with the two equations:

 

Equation 1: x + y = 25000 

*Where did this come from?

⇒The amount invested in each fund will add up to the total amount of money invested

Equation 2: .08x + .085y = 2040 

*Where did this come from?

⇒.08x represents the interest earned on the amount of money invested at 8%, and .085x represents the amount of money invested at the 8.5%. (*remember that you need to move the decimal two places when using percentages)

⇒The total interested earned was $2040, so when we add the interest earned for the first fund (8%) to the interest earned for the second fund (8.5%) it should total up to $2040.

3) Solve the system of equations using method of your choice (elimination or substitution)

I choose to solve the system using substitution because I am more proficient at it and it is easier to explain online, but you can also use elimination or any other method for solving equations.

 

Here are our two equations again

 

x + y = 25000

.08x + .085y = 2040

 

Solve for x (x=25000-y) in first equation and substitute this into the second equation.

 

.08(25000-y) + .085y = 2040

 

Simplify and solve for y.

 

2000 - .08y + .085y = 2040

2000 + .005y = 2040

.005y = 40

y = 8000

 

Since we defined y to be the amount invested in the second (8.5%) fund, that means $8,000 was invested in this fund. The remainder was invested into the 8% fund. To find the remainder we can use the first equation (x+y=25000) or just do 25000-8000. This gives us $17,000 for the amount invested in the 8% fund (or x).

 

To check our answer, plug x and y into both equations to make sure they work.

 

x + y = 17000 + 8000 = 25000   √

.08x + .085y = .08(17000) + .085(8000) = 1360 + 680 = 2040 √

 

Answer: 

 

$17,000 invested into the 8% fund

$8,000 invested into the 8.5% fund