Multiple choice

Sara has \$50,000 to invest. She decides to allocate a portion of it in a secure 4%-interest savings account, while the rest will be invested in a startup venture with her sibling, who pledges to return the investment with a 9% interest. The objective is to generate sufficient interest to contribute to a down payment for a home. What is the minimum amount Sara should invest in the startup venture to guarantee at least \$2,500 in interest?

  1. $5,000
  2. $8,000
  3. $10,000
  4. $15,000
  5. $18,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount in the 9% account. Then (50000-x) is in the 4% account. 0.09x + 0.04(50000-x) >= 2500. 0.09x + 2000 - 0.04x >= 2500. 0.05x >= 500. x >= 10000.

AI explanation

Let the amount invested in the startup venture be x, which means the amount in the savings account is 50000 minus x. Using the simple interest formula, the total interest earned is 9% of x plus 4% of (50000 minus x). This total interest must be at least 2500, so we write the inequality 0.09x + 0.04(50000 minus x) is greater than or equal to 2500. Simplifying this gives 0.05x + 2000 is greater than or equal to 2500, meaning 0.05x is greater than or equal to 500. Solving for x, we find x is greater than or equal to 10000, so the minimum amount is $10,000.

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