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    A sum of ₹8,000 is invested at an annual interest rate of 12% compounded half-yearly for 2 years. Calculate the compound interest earned at the e
    Question

    A sum of ₹8,000 is invested at an annual interest rate of 12% compounded half-yearly for 2 years. Calculate the compound interest earned at the end of 2 years.(Rounded off to the nearest integer)

    A.

    ₹2,200

    B.

    ₹2,100

    C.

    ₹2,150

    D.

    ₹2,280

    Correct option is B

    Given:

    Principal (P) = ₹8,000
    Rate (R) = 12% per annum
    Time (T) = 2 years
    Compounding frequency = Half-yearly (2 times a year)

    Formula Used:
    Compound Interest (CI) = P(1+Rn)ntPP \left(1 + \frac{R}{n}\right)^{nt} - P​​
    Where:
    P = Principal
    R = Annual interest rate (as a decimal)
    n = Number of times the interest is compounded per year
    t = Time the money is invested for, in years

    Solution:
    Here, P = 8,000, R = 12% = 0.12 , t = 2 years, and n = 2 (because interest is compounded half-yearly).

    Substitute these values into the compound interest formula:

    CI = 8000(1+0.122)2×2800000 \left(1 + \frac{0.12}{2}\right)^{2 \times 2} - 8000

    CI = 8000(1+0.06)4800000 \left(1 + 0.06\right)^4 - 8000

    CI = 8000(1.06)4800000 \left(1.06\right)^4 - 8000

    CI =8000×1.2624768000= 8000 \times 1.262476 - 8000

    CI = 10100 - 8000

    CI = 2100

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