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Question

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits 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?


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Solution

Step 1: Finding the total amount at the end of the year:

As, the interest is compounded half yearly,

Therefore, Two times interest will be added on the amount which deposited on 1st January and One time nterest will be added on the amount which deposited on 1st July.

Now, A=P(1+R200)n, where A is the amount at the end of n half years, P is principal amount, R is rate of interest and n is number of half years.

Therefore, total amount at the end of one year on the money deposited on 1st January and 1st July is,

A=16001+52002+16001+52001=16001+1402+16001+1401=1600×41402+1600×41401=1600×4140×4140+1600×4140=1681+1640=3321

Step 2: Finding the interest gained:

Total principal amount deposited in one year =1600+1600=3200

Total amount gained at the end of one year =3321

Therefore, Interest gained =Amount-Principal

=3321-3200=121

Hence, the amount he would have gained by way of interest is 121.


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