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A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

A. Rs. 120

B. Rs. 121

C. Rs. 122

D. Rs. 123

E. None of these

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{Amount}} \cr & = {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \cr & = {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \cr & = {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \cr & = {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \cr & = Rs.\,3321 \cr & \therefore C.I. = Rs.\,\left( {3321 - 3200} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,121 \cr} $$

This Question Belongs to Arithmetic Ability >> Compound Interest

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Comments ( 7 )

  1. Kasahun Ayele
    Kasahun Ayele :
    11 months ago

    Thanks it is good

  2. S Akter
    S Akter :
    1 year ago

    Thanks for the solution.

  3. Tapan Barik
    Tapan Barik :
    2 years ago

    Why we multiple 2 in denominator formula is
    Ci = p(1+r/100)^n+ p

  4. Yakendra Shahi
    Yakendra Shahi :
    2 years ago

    in 1st line
    how 2 x 100 come ??

  5. Md.Asadul Islam
    Md.Asadul Islam :
    2 years ago

    January to june,
    I=pnr
    = 1600*1/2*5/100
    = 40
    Again, june to December
    I=pnr
    = 1640*1/2*5/100
    =41

    2nd case,
    June to December
    I=pnr
    = 1600*1/2*5/100
    = 40

    So, total interest=40+41+40= 121

  6. Himanshu Das
    Himanshu Das :
    3 years ago

    Plz any short tricks

  7. Mangal Poddar
    Mangal Poddar :
    5 years ago

    How time is calculated in a half yearly question

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