Multiple choice

On a sum of money the SI for two years is Rs. $660$, while CI is Rs. $696.30$, the rate of interest being the same in both the cases. The rate of interest is:

  1. $10\%$
  2. $\displaystyle 10\frac{1}{2}$
  3. $12\%$
  4. $11\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For 2 years, SI = 2 * P * R / 100 = 660, so P * R / 100 = 330. CI = P * (1 + R/100)^2 - P = 696.30. P * (2 * R/100 + (R/100)^2) = 696.30. Substituting 330: 2 * 330 + P * (R/100)^2 = 696.30. P * (R/100)^2 = 36.30. (P * R/100) * (R/100) = 36.30. 330 * (R/100) = 36.30. R = 11%.

AI explanation

The difference between compound interest and simple interest for two years equals the interest earned on the first year's simple interest, calculated as (SI/2) * (R/100). Substituting the given values, we get (696.30 - 660) = (660/2) * (R/100), which simplifies to 36.30 = 330 * R / 100. Solving for R yields R = (36.30 * 100) / 330, resulting in an interest rate of 11%.

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