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If an amount becomes 1.21 times itself in 2 years, what is the compound interest rate?

Mathematics

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Answer

(c) 10%\text{(c) } 10\%

Step-by-step solution

4 steps

  1. Identify the given information.

    Let the principal amount be PP.
    The amount after 2 years is A=1.21PA = 1.21P.
    The time period is n=2n = 2 years.
    We need to find the annual compound interest rate RR.

  2. Use the compound interest formula.

    The formula for compound interest is:

    A=P(1+R100)nA = P \left(1 + \frac{R}{100}\right)^n

  3. Substitute the given values into the formula.

    1.21P=P(1+R100)21.21P = P \left(1 + \frac{R}{100}\right)^2

  4. Solve for RR.

    Divide both sides by PP:

    1.21=(1+R100)21.21 = \left(1 + \frac{R}{100}\right)^2

    Take the square root of both sides:

    1.21=1+R100\sqrt{1.21} = 1 + \frac{R}{100} 1.1=1+R1001.1 = 1 + \frac{R}{100}

    Subtract 1 from both sides:

    1.1−1=R1001.1 - 1 = \frac{R}{100} 0.1=R1000.1 = \frac{R}{100}

    Multiply by 100:

    R=0.1×100R = 0.1 \times 100 R=10%R = 10\%

    The annual compound interest rate is 10%10\%. This matches option (c).

    The final answer is (c) 10%\text{(c) } 10\%.

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