Multiple choice

John and Maria make deposits through different schemes at the same bank. John deposits an amount at an interest rate of 5% per annum, while Maria deposits a different amount at an interest rate of 15% per annum. At the end of one year, both receive the same amount of interest. Quantity A The overall interest rate earned by the depositor on the total amount deposited in the bank Quantity B 8%

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P1 and P2 be the amounts deposited. Interest is 0.05*P1 = 0.15*P2, so P1 = 3*P2. The total interest is 0.05*P1 + 0.15*P2 = 0.05*(3*P2) + 0.15*P2 = 0.30*P2. The total principal is P1 + P2 = 4*P2. The overall interest rate is (0.30*P2) / (4*P2) = 0.075 or 7.5%. Since 7.5% < 8%, Quantity B is greater.

AI explanation

Assume John deposits 300 and Maria deposits 100, which makes the interest earned 15 for each at their respective 5% and 15% rates. The total interest is 30 on a total deposit of 400, making the overall interest rate 30/400 x 100 = 7.5%. Since 8% is greater than 7.5%, Quantity B is greater.

Keep practicing — related questions