Use Euler\'s method to solve dB/dt = 0.03 B with initial value B = 1400 when t =

Question

Use Euler's method to solve dB/dt = 0.03 B with initial value B = 1400 when t = 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. A. Delta t = 1 and 1 step: B(1) almostequalto B. Delta t = 0.5 and 2 steps B(1) almostequalto C. Delta t = 0.25 and 4 steps B(1) almostequalto

Explanation / Answer

Eular formula in this case Bt+h = Bt+h f( B,t)

where f(B,t)= 0.03B

a) when h=1

then

at t=0 h=1 give

B(1) = B(0)+h f(B(0) ,0 ) = 1400+1*0.03*1000= 1400+30=1430

b) h=0.5

then

B(0.5)= 1000+0.5*0.03*1000= 1015

B(1)= 1015+0.5*0.03*1015= 1030.225

c)= h=0.25

B(0.25)=1000+0.25*0.03*1000=1007.5

B(0.5)=1007.5+0.25*0.03*1007.5=1015.05625

B(0.75)=1015.05625+0.25*0.03*1015.05625= 1022.669171875

B(1)=1022.669171875+0.25*0.03*1022.669171875= 1030.33919

d)

suppose r=3% =0.03

then intrest in one year= 1000*0.03 *1= 30

Toatal balance = 1000+30=1030

Thus part a correspond to compunding interset once a year

part b corrospond to compound the interest at every 6 month i.e twice a year

part c corrospond to compunding the interest every 4 3 month i.e. 4 times in year

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.