A sum of money becomes Rs. 12,600 after 6 years and Rs. 21,000 after 9 years on compound interest. The sum invested is:

Explanation

Given:A 1 = Rs.12600 T 1 = 6 years A 2 = Rs. 21000 T 2 = 9 years Formula used:Amount (A) = P(1 + r/100) n where, r = rate of interest Calculation:According to question, ⇒ 12600 = P(1 + r/100) 6 ......(i) ⇒ 21000 = P(1 + r/100) 9 .......(ii) From eqn (ii) / eqn (i) ⇒ 21000/12600 = (1 + r/100) 3 ⇒ (5/3) (1/3) = (100 + r)/100 .......(iii) Now from eqn (i) ⇒ 12600 = P(1 + r/100) 6 and from eqn (iii) ⇒ 12600 = P[(5/3) 1/3 ]6 ⇒ 12600 = P(5/3) 2 Principal (P) = 12600 × 9/25 P = Rs. 4536 ∴ Principal is Rs. 4536