Three equal installments, each of Rs. 200, were paid at the end of each year…

When a loan taken at compound interest is repaid through equal yearly installments, the sum borrowed is the amount whose future value — grown at the loan's compound interest rate for the full loan period — exactly equals the combined future value of all the installments, each carried forward (compounded) from its own payment date to the final settlement date.

Applying this to the given loan:

1. Let the sum borrowed be x. Rate r = 20% per annum, compounded annually; the loan runs for n = 3 years; an equal installment A = Rs. 200 is paid at the end of each year.

2. Equate the future value of the principal at the end of year 3 to the combined future value of the three installments, each grown forward from its own payment year to year 3: x(1.20)3 = 200(1.20)2 + 200(1.20)1 + 200(1.20)0

3. Compute each power: (1.20)3 = 1.728, (1.20)2 = 1.44, (1.20)1 = 1.20.

4. Substitute and add: x(1.728) = 200(1.44) + 200(1.20) + 200(1) = 288 + 240 + 200 = 728.

5. Solve for x: x = 728 ÷ 1.728 ≈ 421.30.

Cross-check using the present-value method — discount each installment back to today at the same 20% rate: x = 200/1.20 + 200/(1.20)2 + 200/(1.20)3 ≈ 166.67 + 138.89 + 115.74 ≈ 421.30, which agrees with the future-value calculation above.

So the sum borrowed is Rs. 421.30.