Question

A sum of money triples itself in 3 years at compound interest. In how many years will it become 9 times itself ?

Answer 1

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.