Financial mixture problems

Question

Ethan has a total college account of $175,000. He is going to split this into two different funds, one which pays 6.5% and the other that pays 8%. How much should he put in each account so that he gets the $12,000 in interest per year that he needs to pay for college? 

Answer 1

 

Simple Interest Formula

 

   I = Prt

 

      where I = Interested earned

               P = principal mount invested

               r = interest rate

               r - time (in years) ... for this scenario, t = 1

 

Since we are investing 2 different amounts,

 

   Let x = amount invested at 6.5%

   Let y = amount invested at 8 %

 

The total amount invested is $175,000

 

          x + y = 175,000       (Equation 1)

   .065x + .08y = 12,000     (Equation 2)

 

Using substitution method, solving for y in equation 1, then substituting that into eauation 2 and solving for x,

 

      y = 175,000 - x

 

      .065x + .08y = 12,000

      .065x + .08(175,000 - x) = 12,000

      .065x + 14,000 - .08x = 12,000

 

      -.015x. = 12,000 - 14,000

      -.015x = -2000

      x = -2000/(-0.015)

      x = 133,333.33

 

Since 175.000 - 133,000.33 = 41,666.67

 

$133,333.33 is invested at 6.5 %

$  41,666.66 is invested at 8 %    

 

CHECK:

    6.5% of 133,333.55 = .065(133,333.33) = $8,666.67

         8% of 41,666.66 =   .08(8666.67)     = $3,333.33

                                                   TOTAL  =$12,000