Question

10.3: Problem3 Previous Problem Problem List Next Problem (3 points) Use Euler's method to solve dB dt 0.08B with initial value B 1500 when t A. At 1 and 1 step: B(1) B。Δι = 0.5 and 2 steps: B(1) C. At-0.25 and 4 steps. B(1) 0 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. Note: You can earn partial credit on this problem.

Answer 1

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dB/dt = 0.08B = f(t, B) Euler Method B_i + 1 = B_i + h(0.08 B_i) B_i + 1 = (1 + 0.08h) B_i delta t = 1, B_0 = 1500, t_0 = 0 B(1) = (1 + 0.08)(1500) B(1) = 1620 delta t = 0.5 B(0.5) = (1 + 0.08(0.5) 150 B(0.5) = 1500 B(1) = (1 + (0.08)(0.5))(1500) B(1) = 1622.4 delta t = 0.25 B(0.25) = (1 + (0.08)(0.25) 1500 = 1530 B(0.5) = (1 + (0.08)(0.25))(1530) = 1560.6 B(0.75) = 1591.812 B(1) = 1623.64824 In part d , If B is account balance ..in part a .. Since we take h = 1 ..so this means that interest is credit at the end of period 1 ..so it is compounding interest at once.... In part b and c , we take h = 0.5 and h = 0.25 respectively..so in these cases , we compound interest in 2 and 4 times respectively

In part d , ...

If B is account balance ...in part a ... Since we take h= 1 ...so this means that interest is credit at the end of period 1 ...so it is compounding interest at once....

In part b and c , we take h = 0.5 and h= 0.25 respectively...so in these cases , we compound interest in 2 and 4 times respectively...

So this is compound interest ..because after adding interest , we find next period amount in this new amount...