Hire Purchase / Instalment Plan under CI — Recover equal instalment: A refrigerator costs ₹ 7044 (cash price). A customer pays ₹ 2000 in cash and finances the balance via 3 equal annual instalments at 5% per annum compound interest. What is each instalment amount?

Introduction / Context:
For equal instalments under compound interest, the present value (PV) of all instalments discounted at the contract rate equals the financed amount. This avoids iterative amortization and yields the exact instalment size directly.

Given Data / Assumptions:

• Cash price = ₹ 7044; down payment = ₹ 2000 ⇒ financed amount = ₹ 5044.
• Annual rate i = 5% = 0.05.
• Number of annual instalments n = 3 (end-of-year).

Concept / Approach:
Let each instalment be A. Present value at time 0: PV = A/(1.05) + A/(1.05)^2 + A/(1.05)^3. Set PV = 5044 and solve A = 5044 / [v + v^2 + v^3], where v = 1/1.05.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 1868.28 and ₹ 1865 are rounding/alt-frequency artifacts.
• ₹ 1752, ₹ 1900 do not satisfy PV equality at 5% over 3 years.

Common Pitfalls:

• Using simple interest discounting instead of compound discounting.
• Omitting one of the instalment discount terms.

Final Answer:
Rs. 1852.20.