At the rate of a compound interest rate of 4 years, the

Solution

The sum triples in 4 years. If it becomes 9 times itself, it has tripled twice. This takes 8 years. Let the sum of P, triple in 4 years at R% per annum. P (1 + R/100)⁴ = 3P (1 + R/100)⁴ = 3                … (1) Let it take K years to become 9 times. P (1 + R/100) ^k = 27P 9 = (1 + R/100) ^k [(1 + R/100)⁴] ^k/4 = 3³ 3^k/4 = 3³, K/4 = 3 K = 12 The required result will be 12. Smart Approach- In 4 years =3 times In K year =27 =3³ K =4×3 =12 years.