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    If the interest on a sum of ₹ y at 4% per annum compounded annually for 2 years is ₹612, then the total amount payable at the end of the two-year peri
    Question

    If the interest on a sum of ₹ y at 4% per annum compounded annually for 2 years is ₹612, then the total amount payable at the end of the two-year period will be _____________.

    A.

    ₹8,262

    B.

    ₹7,812

    C.

    ₹8,112

    D.

    ₹8,002

    Correct option is C

    Given:

    Principal amount = ₹y

    Rate of interest = 4% per annum

    Time = 2 years

    Compound interest = ₹612

    Concept Used:

    Compound Interest formula:

    A = P (1+r100)t\left( 1 + \frac{r}{100} \right)^t

    A = 612 + y

    Solution:

    A is the total amount after interest,

    P is the principal amount,

    r is the rate of interest,

    t is the time in years.

    Applying Formula

    612+y=y(1+4100)2 612+y=y(104100×104100) 612+y=y(2625×2625) 612y+yy=(2625×2625) 612y=6766251 612y=676625625 612y=51625 612×62551=y612 + y = y\left( 1 + \frac{4}{100} \right)^2\\ \ \\612 + y = y\left(\frac{104}{100}\times\frac{104}{100} \right)\\ \ \\612 + y = y\left(\frac{26}{25}\times\frac{26}{25} \right)\\ \ \\\frac{612}y + \frac{y}{y} = \left(\frac{26}{25}\times\frac{26}{25} \right)\\ \ \\\frac{612}y = \frac{676}{625} – 1\\ \ \\\frac{612}y = \frac{676-625}{625}\\ \ \\\frac{612}y = \frac{51}{625}\\ \ \\\frac{612\times625}{51} = y

    12×\times​625 = y

    Y = 7500

    Amount After 2 years = CI + P = 7500 + 612 = 8,112

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