Multiple choice

Emily has invested money in two different accounts to fund for her retirement. One account gives her an annual simple interest rate of 4%, while the other provides a rate of 6%. After 3 years, her total income from both investments is $1,200. Additionally, one-half of the amount invested in the first account is equal to one-fourth of the amount invested in the second account. If Emily's total investment is the sum of money invested in these two accounts, how much has she invested in total?

  1. $5,000
  2. $5,800
  3. $6,500
  4. $7,500
  5. $8,000
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D Correct answer
Explanation

Let x and y be the amounts in the two accounts. We have 0.04x*3 + 0.06y*3 = 1200, which simplifies to 0.12x + 0.18y = 1200, or 2x + 3y = 20000. Also, 0.5x = 0.25y, so y = 2x. Substituting y = 2x into the first equation: 2x + 3(2x) = 20000, so 8x = 20000, x = 2500. Then y = 5000. Total investment = 2500 + 5000 = 7500.

AI explanation

Let the amounts invested in the 4 percent and 6 percent accounts be A and B respectively. The condition that half of the first equals a fourth of the second gives 0.5A = 0.25B, meaning B = 2A. Using the total interest formula for 3 years, (A x 4 x 3)/100 + (2A x 6 x 3)/100 = 1200, we find 0.12A + 0.36A = 1200. Solving this gives A = 2500, and since B is double that, the total investment is 2500 + 5000 = 7500.

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