A debt of Rs 7620 is to be discharged by equal annual payments made at the end of each year for 3 years, if interest is charged at 16 2/3% per annum compounded annually. What is the amount of each annual payment?

Introduction:
This is an application of compound interest to loan repayment by equal annual instalments. The idea is that a present debt is equivalent to the present value of a series of future payments, discounted at the given compound interest rate. You must find the fixed instalment that exactly clears the debt in 3 years.

Given Data / Assumptions:

• Present debt (principal) = Rs 7620.
• Number of annual payments = 3.
• Interest rate r = 16 2/3% per annum, which is 1/6 in decimal (approximately 16.67%).
• Interest is compounded annually.
• Payments are made at the end of each year.

Concept / Approach:
Let the annual payment be A. The present value of each payment is obtained by discounting it back to today using the factor 1 / (1 + r)^t. The sum of the present values of all payments must equal the current debt of Rs 7620. We then solve for A using the present value of an annuity formula.

Step-by-Step Solution:
Let r = 1/6 so 1 + r = 7/6.Present value PV of payments: PV = A/(1 + r) + A/(1 + r)^2 + A/(1 + r)^3PV = A / (7/6) + A / (7/6)^2 + A / (7/6)^3PV = A * (6/7 + 36/49 + 216/343)Compute the sum of fractions: 6/7 = 294/343, 36/49 = 252/343, and 216/343 remains as is.Total = (294 + 252 + 216) / 343 = 762 / 343So PV = A * (762/343)Set PV equal to 7620: A * (762/343) = 7620A = 7620 * (343/762) = 10 * 343 = Rs 3430

Verification / Alternative Check:
Check by compounding each payment to the end of 3 years. Payment at end of year 1 grows for 2 more years, payment at year 2 grows for 1 year, payment at year 3 does not grow. The sum of these compounded amounts should equal the future value of the debt after 3 years, confirming that the instalment is correct.

Why Other Options Are Wrong:
Rs 5430, Rs 4430 and Rs 2430: Each of these, when used in the present value equation, does not equal Rs 7620.Rs 2630: This underestimates the payments and would not discharge the full debt with interest.

Common Pitfalls:
Common errors include forgetting to discount each payment to present value or incorrectly treating the interest as simple interest. Another mistake is mixing future value and present value concepts and equating payments directly to the principal without accounting for the time value of money.

Final Answer:
The required equal annual payment to discharge the debt is Rs 3430 per year.