Find the amount of equal installment, annual payment of which will discharge a…

When a debt is repaid through n equal annual instalments under simple interest instead of one lump sum, each instalment paid before the debt's due date effectively earns simple interest for the remaining years until maturity. So the instalment amount X satisfies: 100 × P = X × [100n + r × n(n − 1) / 2], where P is the debt, n the number of years/instalments, and r the annual simple interest rate.

Applying this to the given data (P = Rs. 848, n = 4 years, r = 4% p.a.):

1. 100n = 100 × 4 = 400

2. r × n(n − 1)/2 = 4 × 4 × 3 / 2 = 24

3. Denominator = 400 + 24 = 424

4. Numerator = 100 × P = 100 × 848 = 84800

5. X = 84800 / 424 = 200

Cross-check: value the interest each instalment of Rs. 200 earns up to year 4 and confirm the total equals the debt.

1. Year-1 instalment is outstanding for the remaining 3 years: 200 × (1 + 3 × 4/100) = 200 × 1.12 = 224

2. Year-2 instalment is outstanding for 2 years: 200 × 1.08 = 216

3. Year-3 instalment is outstanding for 1 year: 200 × 1.04 = 208

4. Year-4 instalment earns no further interest: 200

5. Sum = 224 + 216 + 208 + 200 = 848, matching the debt exactly — confirming X = Rs. 200.

Hence the equal annual instalment is Rs. 200.