What equal annual payment will completely discharge a debt of Rs. 7620 due in 3 years at 16 2/3% per annum compound interest?

Introduction / Context:
This question tests the concept of compound interest together with equal annual payments that exactly clear a fixed debt at the end of a given period. The annual payment is treated as an annuity and we must connect its present value with the given debt amount using the given rate of interest.

Given Data / Assumptions:

• Debt to be discharged at the end of 3 years = Rs. 7620.
• Rate of interest = 16 2/3% per annum, taken as 1/6 of the principal each year.
• Payments are equal and made once every year.
• Interest is compounded annually.

Concept / Approach:

We use the present value of an annuity formula. The present value of equal payments A for n years at rate r per year is:

PV = A * {1 - (1 + r)^(-n)} / r

Here, PV must equal the present worth of Rs. 7620 due after 3 years, discounted back to today at the same compound rate of 16 2/3% per annum.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Rs. 5430 and Rs. 4430 produce much larger amounts at the end of 3 years, so the debt would be overpaid. Rs. 2430 produces too small a future value and would leave part of the debt unpaid. Only Rs. 3430 gives a present value equal to the present worth of Rs. 7620 at 16 2/3% per annum.

Common Pitfalls:

A common mistake is to treat 16 2/3% as 16.23% or to apply simple interest formulas instead of compound interest. Another error is to equate the sum of the payments directly to Rs. 7620 without discounting to present value. Learners should always check whether interest is simple or compound and whether payments occur yearly or at some other interval.

Final Answer:

The equal annual payment required to discharge the debt is Rs. 3430.