Arbitrage of SI vs CI at same nominal rate — Net gain over 3 years: Akash borrows ₹ 65000 at 10% per annum simple interest for 3 years and lends the same principal at 10% per annum compound interest for 3 years. What is his gain after 3 years?

Introduction / Context:
Borrowing at simple interest and lending at compound interest at the same nominal rate creates a spread due to interest-on-interest on the lending side. The net gain equals CI received minus SI paid on the identical principal over the same time horizon.

Given Data / Assumptions:

• Principal P = ₹ 65000
• SI outflow: r = 10% = 0.10, t = 3 years ⇒ SI_paid = P * r * t.
• CI inflow: same r and t with annual compounding ⇒ CI_received = P[(1 + r)^t − 1].

Concept / Approach:
Compute both interest totals and subtract: Gain = CI_received − SI_paid. This isolates the compounding advantage over 3 years at 10%.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 1330, ₹ 1300 underestimate the compounding effect; “None of these” is incorrect.

Common Pitfalls:

• Forgetting that SI does not compound; only CI side gains interest on interest.

Final Answer:
₹ 2015.