A bank offers 15% compound interest per half-year (that is, 15% every 6 months). A customer deposits Rs. 7200 on 1st January and another Rs. 7200 on 1st July of the same year. Assuming interest is compounded half-yearly at 15% per half-year, what total amount of interest will he have earned by the end of that year?

Introduction / Context:
This problem involves compound interest with multiple deposits made at different times in the year. The bank pays 15% interest every half-year, so each 6-month period has its own compounding. We must treat each deposit separately, count how many half-year periods it earns interest for, and then sum the interests.

Given Data / Assumptions:

Interest rate = 15% per half-year (every 6 months)
First deposit: Rs. 7200 on 1st January
Second deposit: Rs. 7200 on 1st July
We are asked for total interest earned by 31st December of the same year
Compounding is done half-yearly, so Jan–Jun and Jul–Dec are the two periods

Concept / Approach:
We treat each deposit as a separate principal invested for a certain number of half-year periods. The formula for compound amount for n periods at rate i per period is:
A = P * (1 + i)^n. Interest for that deposit is A − P. The first deposit earns interest for two half-year periods; the second deposit earns interest for only one half-year period. Total interest is the sum of the interests for both deposits.

Step-by-Step Solution:
Let i = 15% = 0.15 per half-year. Deposit 1 (1st January): P1 = 7200, n = 2. A1 = 7200 * (1.15)^2 = 7200 * 1.3225 = Rs. 9522 (approximately). Interest on deposit 1, I1 = A1 − P1 = 9522 − 7200 = Rs. 2322. Deposit 2 (1st July): P2 = 7200, n = 1. A2 = 7200 * 1.15 = Rs. 8280. Interest on deposit 2, I2 = A2 − P2 = 8280 − 7200 = Rs. 1080. Total interest I = I1 + I2 = 2322 + 1080 = Rs. 3402.

Verification / Alternative check:
An alternative is to directly compute the combined amount at the end of the year: A1 + A2 = 9522 + 8280 = 17,802. Total principal deposited is 7200 + 7200 = 14,400. The difference 17,802 − 14,400 = 3,402 rupees. This matches our earlier calculation, confirming the total interest earned.

Why Other Options Are Wrong:
Rs. 850 and Rs. 1701 are far too small compared with what 15% per half-year would generate on Rs. 14,400 over the year. Rs. 6803 is much too large and would imply unrealistically high effective rates or extended compounding periods. Only Rs. 3402 corresponds accurately to the correct compound interest calculation for the two deposits.

Common Pitfalls:
Learners often mistakenly treat the entire Rs. 14,400 as if it were deposited at the start of the year, ignoring the later deposit. Others forget that there are two separate half-year periods and that the first deposit earns interest for both, while the second earns for only one. Keeping a clear timeline of deposits and compounding periods helps avoid these errors.

Final Answer:
The customer earns a total interest of Rs. 3402 by the end of the year.