Answer / Anand Sharma

The given deposit amounts are quarterly (every three months), but the compounding happens half-yearly (every six months). To find the effective annual interest rate, we'll use the formula for compound interest with continuous compounding:
A = P * e^(rt)
where:
A is the final amount
P is the principal (initial deposit)
r is the annual interest rate (5% or 0.05 in decimal form)
t is the time in years (1 year in this case)

First, let's calculate the half-yearly interest:
1st Quarter: A1 = P * (1 + r/2)^(r/2)
2nd Quarter: A2 = P * (A1 * (1 + r/2))^(r/2)
The final amount is: A = A1 + A2 + P

Calculating the half-yearly interest:
A1 = 1600 * (1 + 0.05/2)^(0.05/2)
A2 = A1 * (A1 * (1 + 0.05/2))^(0.05/2)

Total amount: A = A1 + A2 + 1600
The customer would have gained approximately Rs. 389 in interest.

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