Multiple choice

Mia and Ethan invest in a green technology startup. Mia invests \$20,000 for 4 years at a fixed simple interest rate of 7% per annum. Ethan invests the same amount as Mia, dividing it into a ratio of 2 : 3, with one part invested at 5% per annum and the other part at x% per annum for 4 years. If Ethan's total interest is \$400 less than Mia's total interest, what is the value of x?

  1. 6.4%

  2. 7.0%

  3. 7.5%

  4. 8.0%

  5. 8.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mia's interest = 20000 * 0.07 * 4 = 5600. Ethan's investment is split 2:3, so 8000 at 5% and 12000 at x%. Ethan's interest = (8000 * 0.05 * 4) + (12000 * x/100 * 4) = 1600 + 480x. Given Ethan's interest = 5600 - 400 = 5200. 1600 + 480x = 5200. 480x = 3600. x = 3600 / 480 = 7.5%.

AI explanation

Mia's total simple interest is calculated as 20000 * 7 * 4 / 100 = \$5600. Ethan's total interest is \$400 less than Mia's, so Ethan's interest is 5600 - 400 = \$5200. Ethan divides his \$20000 into two parts in a 2 : 3 ratio, which are $8000 and $12000. The interest from the first part at 5% for 4 years is 8000 * 5 * 4 / 100 = $1600. The interest from the second part at x% for 4 years is 12000 * x * 4 / 100 = 480x. Setting the sum of Ethan's interests equal to his total interest gives 1600 + 480x = 5200. Solving for x yields 480x = 3600, so x = 7.5%.

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