The cash price of a TV is Rs. 4022. A customer paid Rs. 1500 in cash and…

Concept

When a balance is repaid through equal instalments under compound interest, the amount owed today equals the sum of the present values of each future instalment — each instalment is discounted back by the compound factor (1 + r) raised to the number of periods before it is paid. Here, the quoted rate is applied directly as the per-instalment discounting rate — the standard convention used for this instalment/debt-repayment problem type, matching the exam's own official working — rather than as a true annualised rate split across the months.

Application

1. Remaining balance after the cash payment: Rs. 4022 − Rs. 1500 = Rs. 2522.

2. Let each monthly instalment be Rs. x. The balance equals the sum of the present values of the three instalments discounted at 5% per period.

3. Balance equation: 2522 = x/1.05 + x/1.052 + x/1.053

4. Evaluating the three discount factors: 1/1.05 = 0.952381, 1/1.052 = 0.907029, 1/1.053 = 0.863838.

5. Adding these factors: 0.952381 + 0.907029 + 0.863838 = 2.723248.

6. So x = 2522 ÷ 2.723248 ≈ Rs. 926.10.

Cross-check

Working backward from x = 926.10 at 5% growth per period: 926.10 ÷ 1.05 = 882.00, which ÷ 1.05 = 840.00, which ÷ 1.05 = 800.00. These three present values sum to 800 + 840 + 882 = Rs. 2522 — exactly the remaining balance — confirming the instalment value.

Reference working (scanned)