Question

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.

Accepted Answer

C. Statement I: Bank A effective annual rate = 6.2% Bank B effective annual rate = $(1 + \frac{3}{100})^2 - 1 = 6.09\%$ Since 6.09% < 6.2%, Bank B pays less total interest each year. Statement I is true. Statement II: If principal doubles in 3 years, in 9 years (3 periods of 3 years), it becomes $2^3 = 8$ times original principal. So $P = 8$, not 9. Statement II is false. Hence, Statement I is true but Statement II is false.

Compound Interest Comparison and Doubling Principal

Explanation

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