Multiple choice

Ruby has a certain amount of money which amounts to Rs. 98,000 in 2 years and Rs. 1,28,000 in 4 years when compounded yearly. Find the rate of interest.

  1. 25%

  2. 20.2%

  3. 18.82%

  4. 14.29%

  5. 13%
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D Correct answer
Explanation

Let P be the principal and r be the rate. We have P(1+r)^2 = 98000 and P(1+r)^4 = 128000. Dividing the second by the first gives (1+r)^2 = 128000/98000 = 128/98 = 64/49. Thus, 1+r = 8/7, so r = 1/7, which is approximately 14.285%.

AI explanation

Let the amount after 2 years be the principal for the next 2 years, so using the compound interest formula, 128000 = 98000 multiplied by (1 plus R by 100) squared. This gives (1 plus R by 100) squared equals 1.30612, so 1 plus R by 100 equals the square root of 1.30612, which is approximately 1.1429. Subtracting 1 and multiplying by 100 yields a rate of 14.29 percent.

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