Multiple choice

At what rate per annum will Rs. 12,167 yield a compound interest of Rs. 3458 in 9 months, interest being compounded quarterly?

  1. 38.70%

  2. 36.70%

  3. 37.5%

  4. 34.8%

  5. 35.5%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principal = 12167, Interest = 3458, Amount = 15625. Time = 9 months = 3 quarters. A = P(1 + r/400)^3. 15625/12167 = (1 + r/400)^3. (25/23)^3 = (1 + r/400)^3. 25/23 = 1 + r/400 => 2/23 = r/400 => r = 800/23 = 34.78%. Matches 34.8%.

AI explanation

The amount is 12167 plus 3458, which equals 15625. Using the compound interest formula, Amount equals Principal multiplied by (1 plus r divided by 400) raised to the power of 36 months divided by 3 months, so 15625 divided by 12167 equals (1 plus r divided by 400) cubed. This yields a quarterly rate of 8.7 percent, meaning the annual rate is 34.8 percent. The result is 34.8 percent.

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