A certain sum of money becomes ₹28800 in 2 years at 20% per annum of compound…

Concept: When interest is compounded annually, a principal P invested at r% per annum grows to A = P × (1 + r/100)n after n years, because each year’s interest is charged on the previous year’s closing balance and not on the original principal. Reading that relation backwards, the principal behind a known amount is recovered by dividing the amount by the whole growth factor: P = A ÷ (1 + r/100)n.

Application: Apply the relation to the figures in this question.

1. Given: amount A = ₹28800, rate r = 20% per annum, time n = 2 years, compounded annually.

2. Growth factor for one year = 1 + 20/100 = 1.2.

3. Growth factor for the full two years = (1.2)2 = 1.44.

4. Principal P = 28800 ÷ 1.44 = ₹20000.

Cross-check: Grow ₹20000 forward year by year at 20%: first-year interest = 20% of 20000 = ₹4000, closing balance ₹24000; second-year interest = 20% of 24000 = ₹4800, closing balance ₹28800 — exactly the amount stated in the question, so the principal is ₹20000.

Common slip: Dividing by a single year’s factor (28800 ÷ 1.2 = ₹24000) undoes only one year of compounding. With n = 2 the amount must be divided by 1.44, not by 1.2.