At what rate of compound interest a sum of money triples in two years then in how many years it will become 27 times?

Let the sum be Rs p, rate be r% per annum.
`3p = p(1+r/100)^(3) rArr (1+r/100)=3^(1//3)`
Now, `9p = p(1+r/100)^(n) rArr (1+r/100)^(n)=9`
`3^(n/3) = 3^(2) rArr n/3 rArr n=6`.
`therefore` In 6 years, the sum becomes 9 times itself.

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Solution

The correct option is A24 yearsP(1+R100)12=3P⇒(1+R100)15=3PP = 3……(i) Let P(1+R100)n=9P⇒(1+R100)n=9⇒(1+R100)n =32⇒(1+R100)n = {(1+R100)12}2 {using(i)}⇒(1+R100)n = (1+R100)24⇒ n = 24Thus, the required time = 24 years.

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