At a ceratain rate of compound interest if a sum of money becomes double in `n` years then find the period of time in which it will become 4-times.

Explanation

Let Rs. `x` becomes double in `n` years at the rate of compound interest `r%` per annum.
`:.x(1+r/100)^(n)=2x`
`implies(1+r/100)^(n)=2`……….1
Also let Rs. `x` becomes 4-tmes in `t` years at the same rate of interest `r%` per annum.
`:.x xx(1+r/100)^(t)=4x`
`implies(1+r/100)^(t)=4`
`implies(1+r/100)^(t)=2^(2)`
`implies(1+r/100)^(t)={(1+r/100)^(n)}^(2)[ :' "by" (1),2=(1+r/100)^(n)]`
`implies(1+r/100)^(t)=(1+r/100)^(2n)`
`=t=2n`
Hence in `2n` years the given principal becomes 4-times.