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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

### 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

1. Thanks it is good

2. Thanks for the solution.

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

4. in 1st line
how 2 x 100 come ??

5. 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. Plz any short tricks

7. How time is calculated in a half yearly question

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