Simple Interest — Reverse present worth via SI discounting: A person closes an investment by withdrawing ₹ 10000 today, ₹ 6000 one year ago, and ₹ 5000 two years ago. Three years ago there was no withdrawal. Assuming 10% p.a. simple interest since opening, what was the approximate initial deposit 4 years ago?

Introduction / Context:
With simple interest, the present worth of withdrawals at different times (counted from opening) uses linear discounting: PV at opening = Withdrawal / (1 + r * t). Summing the present worths of all withdrawals reconstructs the initial deposit, assuming the scheme accrued SI uniformly from the opening on the original principal.

Given Data / Assumptions:

• Annual simple interest r = 10% = 0.10
• Opening was 4 years ago
• Withdrawals: ₹ 5000 at t = 2 years, ₹ 6000 at t = 3 years, ₹ 10000 at t = 4 years
• Goal: approximate initial deposit (no other cash flows)

Concept / Approach:
Under SI, accumulation to a future date uses A = P * (1 + r * t). Conversely, discounting a known future amount W back to opening uses PV = W / (1 + r * t). The initial principal is the sum of the PVs of all withdrawals.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 16500 and ₹ 17280 deviate farther from the computed present worth.
• ₹ 15000 underestimates the required initial deposit.

Common Pitfalls:

• Using compound discounting; SI requires linear discount factors 1 + r * t.
• Mistiming the withdrawals (ensure t = 2, 3, 4 from opening).

Final Answer:
Approximately ₹ 15600.