Multiple choice

A woman invests 70% of her monthly income in a savings account that gives her an annual interest rate of 5%. She decides to invest the remaining 30% in a different account that offers an annual interest rate of 8%. If her monthly income increases by 15% and she keeps the same investment distribution, what is the percentage increase in her total annual interest earned?

  1. 12%

  2. 16%

  3. 15%

  4. 20%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let income be 100. Interest = 0.7*100*0.05 + 0.3*100*0.08 = 3.5 + 2.4 = 5.9. New income = 115. New interest = 0.7*115*0.05 + 0.3*115*0.08 = 4.025 + 2.76 = 6.785. Increase = 6.785 - 5.9 = 0.885. Percentage increase = (0.885/5.9) * 100 = 15%.

AI explanation

Let the initial monthly income be 100. She invests 70 at 5% and 30 at 8%, so her total annual interest is 3.5 + 2.4 = 5.9. When her income increases by 15%, her new income is 115. Keeping the same distribution, she invests 80.5 at 5% and 34.5 at 8%. The new total interest is 4.025 + 2.76 = 6.785. The percentage increase in total interest is ((6.785 - 5.9) / 5.9) * 100, which equals 15%.

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