Multiple choice

The CI on a certain sum for $2$ years is Rs. $410$ and SI is Rs. $400$. The rate of interest per annum is:

  1. $10 \%$
  2. $8 \%$
  3. $5 \%$
  4. $4 \%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years, SI = 2 * P * R / 100 = 400, so PR/100 = 200. CI = P(1 + R/100)^2 - P = 410. P(2R/100 + R^2/10000) = 410. 400 + P(R^2/10000) = 410. P(R/100)^2 = 10. 200 * (R/100) = 10. R/100 = 10/200 = 0.05. R = 5%.

AI explanation

The extra interest earned in compound interest compared to simple interest for two years represents the interest earned on the first year's simple interest, given by the formula Difference = (SI/2) * (R/100). Substituting the given values results in (410 - 400) = (400/2) * (R/100), which simplifies to 10 = 2R. Solving for R gives an interest rate of 5% per annum.

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