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Mathematics

Assertion (A): A = P (1+10100)2\Big(1 + \dfrac{10}{100}\Big)^2 = 1.21P

Reason (R): A = P(1−10100)2P\Big(1 - \dfrac{10}{100}\Big)^2

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are true, and R is the correct reason for A.

  4. Both A and R are true, and R is the incorrect reason for A.

Compound Interest

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Answer

Let P be the principal amount, r% be rate of interest and t be the time.

By formula, A = P (1+r100)t\Big(1 + \dfrac{r}{100}\Big)^t

A = P (1+10100)2=P(1+110)2=(1+0.1)2P=1.12\Big(1 + \dfrac{10}{100}\Big)^2 = P \Big(1 + \dfrac{1}{10}\Big)^2 = (1 + 0.1)^2P = 1.1^2 P = 1.21P

So, assertion (A) is true.

From formula, A = P (1+R100)n\Big(1 + \dfrac{R}{100}\Big)^n

⇒ A = P (1+10100)2\Big(1 + \dfrac{10}{100}\Big)^2

⇒ P = A (1+10100)−2\Big(1 + \dfrac{10}{100}\Big)^{-2}

So, reason (R) is false.

∴ A is true, but R is false.

Hence, option 1 is correct option.

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