Multiple choice

Interest earn on a sum of money at some rate of compound interest for 2 years equal to the interest earn when same sum of money invested at 7% interest in another scheme with S.I. for 3 years. If Interest earn in C.I. for 3 years on same sum of money is Rs. 1655, then find out the initial sum of money.

  1. 4500

  2. 5400

  3. 5000

  4. 6000

  5. 5500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal. CI for 2 years at r% = P((1+r/100)^2 - 1). SI for 3 years at 7% = P * 3 * 0.07 = 0.21P. Equating: (1+r/100)^2 - 1 = 0.21. (1+r/100)^2 = 1.21. 1+r/100 = 1.1, so r = 10%. Now, CI for 3 years at 10% = P((1.1)^3 - 1) = P(0.331) = 1655. P = 1655 / 0.331 = 5000.

AI explanation

Let the compound interest rate be R, so equating the interests gives P times R plus R squared divided by 100 equal to P times 7 times 3 divided by 100. Solving for R reveals that the compound interest rate is 10%, because 10 plus 1 equals 11, which makes the two year interest 21% of P, matching the 21% simple interest. The compound interest for 3 years at 10% is calculated as P times 0.331, which equals 1655 rupees, making the principal sum 5000 rupees.

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