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Identify the compound interest for the first year (CI1) and the second year (CI2).

Chemistry

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Answer

15% P.C.P.A.15\% \text{ P.C.P.A.}

Step-by-step solution

5 steps

Q. The Compound interest of certain for first and Second year is Rs. 20 and Rs. 23 respectively. Find the rate of interest in P.C.P.A.

  1. Identify the compound interest for the first year (CI1CI_1) and the second year (CI2CI_2).

    CI1=Rs. 20CI_1 = \text{Rs. } 20 CI2=Rs. 23CI_2 = \text{Rs. } 23

  2. Calculate the additional interest earned in the second year.

    This additional interest is the interest earned on the first year's interest.

    Additional Interest=CI2−CI1=23−20=Rs. 3\text{Additional Interest} = CI_2 - CI_1 = 23 - 20 = \text{Rs. } 3

  3. Consider the first year's compound interest (CI1CI_1) as the principal for calculating the additional interest.

    The time period for this additional interest is 1 year.
    Principal (PP) = Rs. 20
    Interest (II) = Rs. 3
    Time (TT) = 1 year

  4. Use the simple interest formula I=P×R×T100I = \frac{P \times R \times T}{100} to find the rate of interest (RR).

    3=20×R×11003 = \frac{20 \times R \times 1}{100}

  5. Solve for RR.

    3=20R1003 = \frac{20R}{100} 3=R53 = \frac{R}{5}

    Multiply both sides by 5:

    R=3×5R = 3 \times 5 R=15R = 15

    The rate of interest is 15% per annum.

    The final answer is 15% P.C.P.A.15\% \text{ P.C.P.A.}.

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