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Use Euler's method to solve $\frac{dB}{dt}= 0.05 B$ with initial value $B=800$ when $t=0$ .

A. $\Delta t = 1$ and 1 step: $B(1) \approx$

B. $\Delta t = 0.5$ and 2 steps: $B(1) \approx$

C. $\Delta t = 0.25$ and 4 steps: $B(1) \approx$

D. Suppose $B$ is the balance in a bank account earning interest. Be sure that you can explain why the result of your calculation in part (a) is equivalent to compounding the interest once a year instead of continuously. Then interpret the result of your calculations in parts (b) and (c) in terms of compound interest.