Multiple choice

The difference between the amount of compound interest and simple interest accured on an amount of Rs. $26000$ at the end of $3$ years is Rs. $2994.134$. What is the rate of interest ?

  1. $22 \%$
  2. $17 \%$
  3. $19 \%$
  4. $24 \%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 3 years, the difference between compound interest and simple interest is given by the formula D = P * (r/100)^2 * (3 + r/100). Plugging in D = 2994.134 and P = 26000, we solve for r. Testing 19 percent: 26000 * (0.19)^2 * (3.19) = 26000 * 0.0361 * 3.19 = 2994.134.

AI explanation

Using the formula for the difference between compound interest and simple interest for 3 years, Difference = P times (R/100) cubed + 3 times P times (R/100) squared divided by 100. Here, 2994.134 = 26000 times ( (1 + R/100) cubed - 1 - (3R/100) ). Testing the given rate of 19%, the calculation is 26000 times (1.19 cubed - 1 - 0.57). This simplifies to 26000 times (1.685159 - 1.57) = 26000 times 0.015159, which equals 2994.134.

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