Investment problem

Question

Katy invests a total of $17,000 in two accounts. The first account earned a rate of return of 13% (after a year). However, the second account suffered a 7% loss in the same time period. At the end of one year, the total amount of money gained was $1,010.00. How much was invested into each account?

Answer 1

x represents the amount at 13%

17000 - x represents the amount at - 7%

0.13x + (-0.07)(17000 - x)) = 1010

0.13x - 1190 + 0.07x = 1010

0.2x = 2200

x = 11000

Answer 2

Investment problem: Katy invests a total of $17,000 in two accounts. The first account earned a rate of return of 13% (after a year). However, the second account suffered a 7% loss in the same time period. At the end of one year, the total amount of money gained was $1,010.00. How much was invested into each account?

Detailed Solution:

First Account - Amount: $x & Interest: $0.13x Second Account - Amount: $y & Interest: -$0.07y

Amount: x + y = 17,000 ==> Equation 1

Interest: 0.13x – 0.07y = 1,010 ==> Equation 2

In TI-84 Plus, create 2 x 3 Matrix A of above Equations, do the math: Matrix ==> Math ==> rref([A])

rref([A]) gives you the solution: x = 11,000 and y = 6,000

First Account - Amount: x = $11,000 & Interest: $0.13(11,000) = $1,430

Second Account - Amount: y = $6,000 & Interest: -$0.07(6,000) = -$420

Check:

Amount: x + y = 17,000 ==> 11,000 + 6,000 = 17,000 ==> 17,000 = 17,000

Interest: 0.13x – 0.07y = 1,010 ==> 0.13(11,000) – 0.07(6,000) = 1,010 ==> 1,010 = 1,010