Multiple choice

The C.I. on a certain sum for $2 $ years is Rs $410$ and S.I. is Rs $400.$ What is the rate of interest per annum?

  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 P * R / 100 = 200. CI = P * (1 + R/100)^2 - P = 410. Substituting P*R/100 = 200 into the CI formula: 200 + P * (R/100)^2 = 410, so P * (R/100)^2 = 210. Dividing the two equations: (P * R^2 / 10000) / (P * R / 100) = 210 / 200, so R/100 = 1.05, R = 5%.

AI explanation

Using the successive percentage formula for compound interest, the difference between the compound interest and simple interest for two years equals P(R/100)^2. Since the simple interest for two years is 400, the principal times the rate is 20000, and the difference of 410 - 400 = 10 means 20000(R/100)^2 = 10. Solving for R^2 = 25 gives R = 5, so the rate of interest per annum is 5%.

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