A bank offers 5% compound interest calculated half-yearly. A customer deposits Rs. 1600 on 1 January and another Rs. 1600 on 1 July of the same year. What is the total interest earned by 31 December of that year?

Problem restatement
Interest is compounded twice a year at 5% p.a. (i.e., 2.5% per half-year). Two equal deposits are made: one on 1 Jan (earns two half-years), and one on 1 Jul (earns one half-year). Find the total interest by year end.

Given data

• Rate per half-year = 5% ÷ 2 = 2.5% = 0.025
• Deposit 1: Rs. 1600 on 1 Jan → 2 half-years
• Deposit 2: Rs. 1600 on 1 Jul → 1 half-year

Concept/Approach
Treat each deposit as a separate principal for its own compounding duration and then sum the interests.

Step-by-step calculation
Interest on 1st deposit = 1600[(1 + 0.025)² − 1]= 1600(1.050625 − 1) = 1600 × 0.050625 = 81.00Interest on 2nd deposit = 1600[(1 + 0.025) − 1] = 1600 × 0.025 = 40.00Total interest = 81.00 + 40.00 = Rs. 121

Verification/Alternative
Amount of 1st deposit at year end = 1600 × 1.050625 = 1681.00 (so interest 81.00). Amount of 2nd deposit = 1600 × 1.025 = 1640.00 (so interest 40.00). Sum of interests = 121.00.

Common pitfalls
Applying 5% for the July deposit (should be 2.5% for one half-year), or compounding both deposits for two periods.

Final Answer
Rs. 121