Multiple choice

Given below are two statements: Statement I: A savings account at Bank A pays 6.2% interest, compounded annually. Bank B's savings account pays 6% compounded semi-annually. Bank B is paying less total interest each year. Statement II: A sum of money at a certain rate of compound interest doubles in 3 years. In 9 years, it will be P times original principal. Then P = 9. In the light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true but Statement II is false.

  4. Statement I is false but Statement II is true.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Bank A effective rate = 6.2%. Bank B effective rate = (1 + 0.06/2)^2 - 1 = 1.03^2 - 1 = 0.0609 or 6.09%. 6.2% > 6.09%, so Bank B pays less. Statement I is true. Statement II: A(1+r)^3 = 2A, so (1+r)^3 = 2. In 9 years, A(1+r)^9 = A((1+r)^3)^3 = A(2^3) = 8A. So P = 8, not 9. Statement II is false.

AI explanation

For Statement I, Bank A pays an effective annual rate of 6.2%, while Bank B pays a semi-annual rate of 3%, giving an effective annual rate of (1.03)^2 - 1 = 6.09%, meaning Statement I is true because 6.09% is less than 6.2%. For Statement II, using the compound interest formula, if a sum doubles in 3 years, it grows by a factor of (2)^3 = 8 over 9 years, meaning P = 8, so Statement II is false. Therefore, Statement I is true but Statement II is false.

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