Multiple choice

A sum of money, invested at compound interest, amounts to Rs. $19,360 $ in $2$ years and to Rs. $23,425.60$ in $4$ yeas. Find the rate per cent and the original sum of money.

  1. $10$% and Rs. $17,000$
  2. $19$% and Rs. $25,637$
  3. $10$% and Rs. $16,000$
  4. $19$% and Rs. $26,634$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The amount after 2 years is P(1+r)^2 = 19360, and after 4 years is P(1+r)^4 = 23425.60. Dividing the two gives (1+r)^2 = 23425.60 / 19360 = 1.21. Thus, 1+r = 1.1, so r = 10%. P = 19360 / 1.21 = 16000.

AI explanation

Using the compound interest formula, the amount after 4 years divided by the amount after 2 years gives the square of the growth factor for one year. Dividing 23425.60 by 19360 gives 1.21, meaning the yearly growth factor is 1.10 and the rate is 10%. Applying this rate backward for 2 years to find the original principal, the equation is 19360 = P(1.10)^2; solving for P gives 19360 / 1.21, which is 16000.

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