A man borrows Rs. 2100 and undertakes to pay back with compound interest @ 10%…

Concept: When a loan is repaid in equal yearly installments under compound interest, the principal borrowed must equal the sum of the present values of every installment, each installment discounted back to the day of borrowing at the loan's interest rate for the number of years before it falls due. For two equal yearly installments of amount x at rate r, this gives:

Principal = x/(1+r) + x/(1+r)2, so the lender receives the same value whether the loan is repaid at once or across installments.

Applying to this question: Principal = Rs. 2100, rate r = 10% = 0.1, and both yearly installments are equal to some amount x, so:

2100 = x/1.1 + x/1.21

1. Write the present-value equation: 2100 = x/1.1 + x/1.21.

2. Express each present-value factor as a fraction: 1/1.1 = 10/11 and 1/1.21 = 100/121.

3. Add the fractions over a common denominator: 10/11 + 100/121 = 110/121 + 100/121 = 210/121.

4. Substitute back into the equation: 2100 = x × 210/121.

5. Solve for x: x = 2100 × 121/210 = 10 × 121 = 1210.

Cross-check: Using the reducing-balance method — at the end of year 1 the loan grows to 2100 × 1.1 = 2310. Paying an installment of 1210 leaves an outstanding balance of 2310 − 1210 = 1100. This balance grows to 1100 × 1.1 = 1210 by the end of year 2, which is exactly the second installment — so the loan is fully cleared with nothing left over.

Answer: Each yearly installment is Rs. 1210.