system of equations

Question

The given amount of annual interest is earned from a total of $12,000 invested in two funds paying simple interest. what are the two amounts when $366 is the annual interest and the two interest rates are 2.4% and 3.7%?

Answer 1

Hi Tory,

The given amount of annual interest is earned from a total of $12,000 invested in two funds paying simple interest. what are the two amounts when $366 is the annual interest and the two interest rates are 2.4% and 3.7%?

Given:

$12000 total invested

Simple Interest

Fund 1 2.4% interest, Fund 2 3.7% interest

Annual Interest is $366

Find: What are the two amounts invested into each fund?

Looking at this problem it tells us that we will be using a simple interest equation to determine the annual interest.

I = P r t I=interest P=principle r = rate t = time

Our time is 1 year. our rates are 2.4% and 3.7% for a year.

Let x = Amount of money invested in Fund 1

Let y = amount of money invested in Fund 2

We have 2 unknowns, therefore we will need two equations to determine the values.

From the above, we know that the total invested is 12,000

So x + y = total amount x + y = 12000 This is the 1st equation.

We are given the interest rate of each fund and the time of the investment

I=Prt

For Fund 1 I₁ = (x) (0.024) (1)

Fund 2 I₂ = (y)(0.037)(1)

I₁ + I₂ = 366 (From above it says total interest earned was 366)

(x) (0.024) (1) + (y)(0.037)(1) = 366 This is our 2nd equation

Now you can choose your method to solve the system of equations.

I will use substitution

x + y = 12000

(x) (0.024) + (y)(0.037) = 366

y = 12000-x

0.024 x + (12000-x)(0.037) = 366

0.024x - 0.037x + 444 = 366

x = 6000

y = 12000 - 6000 = 6000

So 6000 was invested in both funds.

We can check our work to determine if our answer is correct

I₁ + I₂ = 366

(6000)(0.024) + 6000(0.037) = ? 366

366 = 366 The answer checks out

Let me know if you need more help!