* Use Matlab Use the ode45 application to solve the following: Suppose that you

Question

* Use Matlab

Use the ode45 application to solve the following: Suppose that you deposit some money in a bank that pays interest at an annual rate r. The value of the investment at any time, t, is S(t). If the interest is compounded continuously we can use a simple differential equation to describe the investment growth. The rate of change of the investment, dS/dt, is the interest rate, r, times the value of the investment, S(t). So dS/dt = rS and we can assume an initial value, S(0) = S_0. If r = 8% and So = exist1000, use MATLAB to determine the investment value after 10 years.

Explanation / Answer

dS/dt = rS

dS/S = rdt

integrating both sides

ln (S) |S(t) & S(0) = r t |t & 0

ln (S / S0) = r t

S = S0 x ert

S = $1000 X e8% x 10

S = $2225.541

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