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Mathematics

Consider the following two statements.

Statement 1: A sum of ₹ 1,000 invested at 10% p.a. rate of interest will earn ₹ 100 interest in first year.

Statement 2: Simple and compound interest is the same for first conversion period at the same rate of interest.

Which of the following is valid?

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and Statement 2 is false.

  4. Statement 1 is false, and Statement 2 is true.

Compound Interest

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Answer

Given,

P = ₹ 1,000

R = 10%

T = 1 year

Using C.I. formula,

C.I. = P[(1+R100)n−1]P\Big[\Big(1 + \dfrac{R}{100}\Big)^n - 1\Big]

Substituting the values, we get

C.I.=1,000×[(1+10100)1−1]=1,000×[(1+110)−1]=1,000×(1+110−1)=1,000×(110)=100.C.I. = 1,000 \times \Big[\Big(1 + \dfrac{10}{100}\Big)^1 - 1\Big]\\[1em] = 1,000 \times \Big[\Big(1 + \dfrac{1}{10}\Big) - 1\Big]\\[1em] = 1,000 \times \Big(1 + \dfrac{1}{10} - 1\Big)\\[1em] = 1,000 \times \Big(\dfrac{1}{10}\Big)\\[1em] = 100.

Calculating S.I.,

P = ₹ 1,000

R = 10%

T = 1 year

Using formula,

S.I. = P×R×T100\dfrac{P \times R \times T}{100}

Substituting the values, we get

⇒S.I.=1,000×10×1100=10×10=100.\Rightarrow S.I. = \dfrac{1,000 \times 10 \times 1}{100}\\[1em] = 10 \times 10 \\[1em] = 100.

Since,

C.I. = S.I. = ₹ 100.

Therefore, we can say that simple and compound interest is the same for first conversion period at the same rate of interest.

∴ Both statements are true.

Hence, option 1 is the correct option.

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