Question: Use Euler’s method to solve \(\frac{d B}{d t}=0.05 \mathrm{~B}\) with

initial value \(B=1000\) when \(t=0\). Take:

1. \(\Delta t=1\) and 1 step
2. \(\Delta t=0.5\) and 2 steps
3. \(\Delta t=0.25\) and 4 steps.
4. Suppose \(B\) is the balance in a bank account earning interest. Explain why the result of your calculation in part (a) is equivalent to compounding the
   interest once a year instead of continuously.
5. Interpret the result of your calculations in part (b) and (c)$ in terms of compound interest.

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