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Lecture 12 Presentation and Example

# Lecture 12 Presentation and Example - Compound Interest...

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Click to edit Master subtitle style Compound Interest: Example of Numerical Solution to 1st Order ODE Prof. Dragan Djurdjanovic ME 218 Fall 2008 11

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Recapitulation: Euler’s Method 22
Recapitulation: Heun’s Method Equivalent to Taylor Series Expansion up to (and including) 2nd order terms (involves numerical approximations of 2nd order derivatives) 33

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4th Order Runge-Kutta (RK) Method Equivalent to Taylor Series Expansion up to (and including) 4th order terms (involves numerical approximations of 4th order derivatives) 44
The Problem n A sum of P= \$5,000 (P) is deposited in a bank n The bank pays an interest of r = 5% per annum. n Assume that additional funds are deposited continuously at the rate of c = \$1,000 per annum n What is the value of the investment at the end of k = 10 years, assuming that the interest is compounded continuously ? 55

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The Differential Equation n Let the value of the investment at time ‘t’ be X. n
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Lecture 12 Presentation and Example - Compound Interest...

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