Multiple choice

Ramlal deposited โ‚น1800 in each of two different schemes, both paying ๐‘Ÿ% interest per annum, one under simple interest, and the other under compound interest, compounded per annum. If the difference between the two amounts that he'll receive at the end of two years is โ‚น12.50, find the value of ๐‘Ÿ.

  1. 5%

  2. 6.25%

  3. 7.5%

  4. 8.33%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SI = (1800 * r * 2) / 100 = 36r. CI = 1800 * (1 + r/100)^2 - 1800 = 1800 * (2r/100 + r^2/10000) = 36r + 0.18r^2. Difference = 0.18r^2 = 12.50. r^2 = 12.50 / 0.18 = 69.44. r = sqrt(69.44) = 8.33%.

AI explanation

The formula for the difference between compound interest and simple interest on a principal P for two years at rate r is Difference = P * r^2 / 100^2. Substituting the given values yields 12.50 = 1800 * r^2 / 10000. Solving for r^2 gives 125/18, so the rate r is the square root of 6.944, which equals 8.33%.

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