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    A sum of  Rs. 21,000 is borrowed at a rate of 10% p.a. compound interest compounded yearly. It is returned in two equal annual instalments W
    Question

    A sum of  Rs. 21,000 is borrowed at a rate of 10% p.a. compound interest compounded yearly. It is returned in two equal annual instalments What is the amount of each installment?

    A.

    Rs. 12,000

    B.

    Rs. 12,100

    C.

    Rs. 12,250

    D.

    Rs. 12,150

    Correct option is B

    Given:

    Principal (P) = Rs. 21,000

    Rate of Interest (R) = 10% per annum

    Number of Instalments (n) = 2

    Formula Used:

    P = x(1+R100)+x(1+R100)2++x(1+R100)n\frac{x}{(1 + \frac{R}{100})} + \frac{x}{(1 + \frac{R}{100})^2} + \dots + \frac{x}{(1 + \frac{R}{100})^n}​​

    Solution:

    Substituting the values:

    21,000=x1.1+x1.2121,000 = \frac{x}{1.1} + \frac{x}{1.21}​​

    21,000=x(11.1+11.21)21,000 = x \left( \frac{1}{1.1} + \frac{1}{1.21} \right)​​

    21,000=x(1.1+11.21)21,000 = x \left( \frac{1.1 + 1}{1.21} \right)​​

    21,000=x(2.11.21)21,000 = x \left( \frac{2.1}{1.21} \right)​​

    x=21,000×1.212.1x = 21,000 \times \frac{1.21}{2.1}​​

    x=21,000×121210×1x = \frac{21,000 \times 121}{210 \times 1}​​

    x=100×121x = 100 \times 121​​

    x = Rs. 12,100

    Thus, Each instalment is Rs.12,100 

    Alternate Solution: 

    Rate of interest = 10% = 110\frac{1}{10} 

    210 unit  = 21000 

    so, 121 unit = 21000210×121=12100\frac{21000}{210} \times 121 = ₹12100​​

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