In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?

Explanation

Let at any time `t`, prinicipal `=P`,
`:. (dP)/(dt)=(5)/(100)xxP=(P)/(20)`
`implies (dP)/(P)=(dt)/(20)`
`implies logP=(1)/(20)t+c_(1)`
`implies P=e^(t//20)*e^(c_(1))`
`implies P=c*e^(t//20)` [Where `c=e^(c_(1))`]
Now at `t=0`, `P=1000`
`:. 1000=c*e^(0)`
`implies c=1000`
`:. P=1000*e^(t//20)`
Let the principal will be doubles i.e., `2000rs` in `t` years.
`:. 2000=1000*e^(t//20)`
`implies e^(t//20)=2`
`implies (t)/(20)=log2`
`implies t=20 log2`.