Multiple choice

Emma and Noah are both investing in a sustainable energy initiative. Emma invests \$15,000 for 3 years at a fixed interest rate of 10% per annum. Meanwhile, Noah invests the same amount, \$15,000, for 3 years but divides his investment into three different parts in the ratio 3 : 5 : 7, earning interest rates of 8%, 10%, and x%, respectively. It is known that the total interest earned by Noah is 5% less than the interest earned by Emma. What is the value of x?

  1. 10.79%

  2. 9.79%

  3. 8.45%

  4. 7.83%

  5. 5.84%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Emma's interest = 15000 * 0.10 * 3 = 4500. Noah's interest = 4500 * 0.95 = 4275. Noah's investment parts: 3k+5k+7k = 15k = 15000, so k=1000. Parts are 3000, 5000, 7000. Interest = 3000*0.08*3 + 5000*0.10*3 + 7000*x*3 = 4275. 720 + 1500 + 21000x = 4275. 21000x = 2055. x = 2055/21000 = 0.097857... or 9.79%.

AI explanation

Using the simple interest formula, Emma's interest is 15000 times 10 times 3 divided by 100, which equals \$4,500. Noah's total interest is 5% less than Emma's, making his interest 4500 minus 225, which is \$4,275. Noah's investment parts in the ratio 3:5:7 of 15000 are $3,000, $5,000, and $7,000, generating $720, $1,500, and 210x in interest respectively. Setting the sum of Noah's interest equal to 4275 gives 2220 + 210x = 4275, so x is 2055 divided by 210, which equals approximately 9.79%.

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