[B] A loan of $210000 is repaid over 20 years by monthly payments of $1575. Use two iterations of the Newton-Raphson method starting with the initial guess of an annual interest rate of 12% (compounded monthly), to determine the annual interest rate. NOTE: IfP is borrowed at a rate of r per period, and is repaid over N periods by payments of Y, then: Pr + Y[(1+r)-N – 1] = 0 If f(r) = 210000r + 1575[(1+r) 400 – 1] and f'(r) = k – a(1+ br) €, then: k =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.