A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

Question: A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

Solution:
let,
the sum = P

ATQ,
3P = P(1 + r)⁶
⇒ (1 + r)⁶ = 3

Again,
let, sum will 27 times in n years

Then,
27P = P(1 + r)ⁿ
⇒ 27 = (1 + r)ⁿ
⇒ 3³ = (1 + r)ⁿ
⇒ {(1 + r)⁶}³ = (1 + r)ⁿ
⇒ (1 + r)¹⁸ = (1 + r)ⁿ
∴ n = 18