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:
Compound Interest Calculation
Given values:
Principal amount deposited on 1st January = Rs. 1600
Principal amount deposited on 1st July = Rs. 1600
Rate of interest = 5% per annum (2.5% half-yearly)
Time = 1 year (2 half-years)
Interest for the first half-year (January to June):
Principal = Rs. 1600
Interest rate = 2.5%
Interest = (1600 × 2.5) / 100 = Rs. 40
Amount at the end of the first half-year (June 30th):
= Principal + Interest
= 1600 + 40
= Rs. 1640
Interest for the second half-year (July to December):
Principal = Rs. 1640 (initial deposit) + Rs. 1600 (second deposit) = Rs. 3240
Interest rate = 2.5%
Interest = (3240 × 2.5) / 100 = Rs. 81
Amount at the end of the year:
= Principal + Interest
= 3240 + 81
= Rs. 3321
Total interest earned for the year:
= Amount at the end of the year – Total principal deposited
= 3321 – (1600 + 1600)
= 3321 – 3200
= Rs. 121
The customer would have gained Rs. 121 by way of interest.
