If is known that, if the interest i s compounded continuously, the principal changes f the rate equal to the product of the rate of bak interest per annum, and the principal. If the interest is compounded continuously at 5% per annum, in how many years will Rs. 100 double itself? At what interest rate will Rs. 100 double itself in 10 years `((log)_e2=0. 6931)` How much will Rs. 1000 be worth at 5% interest after 10 years? `(e^(0. 5)=1. 648)dot`

Explanation

To solve the problem step by step, we will break it down into three parts as per the question.

### Part 1: Doubling Rs. 100 at 5% interest compounded continuously

1. **Understanding the formula**: The formula for continuous compounding is given by:
\[ \frac{dP}{dt} = rP \]
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