A sum of money becomes 2-times at the rate of compound interest in 15 years. In how many years, it will becomes 8 times at the same of compound interest?

Explanation

Let the principal be Rs.x and the rate of compound interest per annum be r%.
`:.` The amount of Rs.x in 15 years at the rate of compound interest of r% per annum
`=Rs.x(1+r/100)^(15)`
As per question `x(1+r/100)^(15)=2ximplies(1+r/100)^(15)=2`..........1
Now let the principal becomes 8-times in t -years at the same rate of compound interest.
`:.x(1+r/100)^(t)=8ximplies(1+r/100)^(t)=8`
`implies(1+r/100)^(t)=2^(3)`
`implies(1+r/100)^(5)={(1+r/100)^(15)}^(3)[ :' 2=(1+r/100)^(15)` by 1`]`
`implies(1+r/100)^(t)=(1+r/100)^(45)`
`impliest=45`
Hence the required time `=45` years.