Multiple choice

The difference between S.I. and C.I. (compounded annually) on a sum of 64000 for 2 years is 1000. What is the rate of interest per annum?

  1. $25$%
  2. $\displaystyle16\frac{2}{3}\%$
  3. $\displaystyle13\frac{1}{3}\%$
  4. $\displaystyle12\frac{1}{2}\%$
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D Correct answer
Explanation

For 2 years, the difference between CI and SI is P * (r/100)^2. Here, 1000 = 64000 * (r/100)^2. 1000/64000 = (r/100)^2, so 1/64 = (r/100)^2. Taking square roots, 1/8 = r/100. r = 100/8 = 12.5%.

AI explanation

Applying the two-year difference formula, Difference equals Principal times R squared divided by 10000. Plugging in the values gives 1000 equals 64000 times R squared divided by 10000. This simplifies to 1000 equals 6.4 times R squared, meaning R squared is 156.25; therefore, the rate of interest per annum is 12.5 percent.

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