Find the sum of money which will amount to ₹26010 in 6 months at the rate of…

Concept — For compound growth, the amount after n periods is A = P(1 + r/100)n, where r is the rate for ONE compounding period and n is the number of such periods. Quarterly compounding means the yearly rate is split into four equal periods, one for every three months. Recovering the principal from a known amount simply inverts this relation: P = A ÷ (1 + r/100)n.

Application

1. Rate per compounding period: 8% per annum ÷ 4 = 2% per quarter, so one quarter multiplies the balance by 1.02.

2. Number of periods: 6 months contains 2 quarters, so n = 2.

3. Write the relation for the two quarters: A = P × (1.02)2 = P × 1.0404.

4. Substitute the given amount: 26010 = P × 1.0404.

5. Solve for the principal: P = 26010 ÷ 1.0404 = 25000.

Cross-check

• Forward check: ₹25000 plus 2% gives ₹25500 at the end of the first quarter, and ₹25500 plus 2% gives ₹26010 at the end of the second — exactly the amount stated in the question.

• Contrast with a non-compounded reading: treating the 6 months as a single 4% period gives the divisor 1.04 and a principal of about ₹25009.60. The interest earned on the first quarter's interest is what makes the correct divisor 1.0404 instead of 1.04.

Hence the required sum of money is ₹25000.