How to find how much is invested in a certain amount of money

Question

$12,000 is invested in a money market certficate, part at 11% interest and part at 13%. If the total interest from both investments is $1490, how much is invested at 13% interest?

Answer 1

Hi Samantha,

 

Let's begin by assigning two letters to represent our two unknowns:

    x = amount invested at 11%

    y = amount invested at 13%

 

Next, let's write two equations which we can use to solve for our two unknowns:

    Equation #1 (based upon total amount invested):

        x + y = 12,000

    Equation #2 (based upon total interest earned):

        0.11x + 0.13y = 1,490

 

Next, let's substitute an expression for y in terms of x from Equation #1 and plug it into Equation #2 and solve for x:

    x + y = 12,000 (Equation #1):

          y = 12,000 - x

    0.11x + 0.13y = 1,490 (Equation #2)

    0.11x + 0.13(12,000 - x) = 1,490 (y in terms of x)

    0.11x + 1,560 - 0.13x = 1,490

    1,560 - 0.02x = 1,490

    0.02x = 1,560 - 1,490

    0.02x = 70

    x = 70/0.02

    x = $3,500 (amount invested at 11%)

 

Next, let's plug in our value for x into Equation #1 and solve for y:

    x + y = 12,000 (Equation #1)

    3,500 + y = 12,000 (plugged in value for x)

    y = 12,000 - 3,500

    y = $8,500 (amount invested at 13%)

 

Finally, we can plug in both investment amounts into Equation #2 and see if the sum of their earned interest amounts is equal to our given total earned interest amount.

    0.11x + 0.13y = 1,490 (Equation #2)

    0.11(3,500) + 0.13(8,500) = 1,490 (plug-ins)

    385 + 1,105 = 1,490

    1,490 = 1,490 (sum = total)

 

Since the sum of the earned interest amount for each investment amount is equal to the total earned interest amount, we are confident that our answer for each investment amount is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.