In a bank, principal increases continuously at the rate of 5% per year. An amountof Rs 1000 is deposited with this bank, how much will it worth after 10 years`(e^(0. 5)=1. 648)`

Explanation

Let the principal and time be `P` and `t` respectively.
then given that, `(dp)/(dt)=5%` of `Pimplies(dp)/(dt)=(5)/(100)P`
`implies (dp)/(P)=(1)/(20)dt`
`implies int(dp)/(P)=int(1)/(20)dtimplieslog|P|=(1)/(20t+C`…….`(1)`
Initially, at `t=0`, `P=1000`
`:. log 1000=0+cimplies log1000`
put the value of `C` in equation `(1)`,
`log|P|=(1)/(20)t+log1000`
`implies log|((P)/(1000))|=(1)/(20)t`
when `t=10` then `log|(P)/(1000)|=(1)/(20)xx10=(1)/(20)`
`implies (P)/(1000)=e^(1//2)`
`implies (P)/(1000)=e^(1//2)`
`implies (P)/(1000)=e^(0.5)=1.648`
`implies P=1000xx1.648impliesP=1648`
Therefore, the sum will become `1648rs` in `10` years.