Differential Equation Modeling Question

[jofree87]

The differential equation dS/dt = kS + D represents the rate of change of savings when S = savings balance, k = interest rate, and D = deposit.

Ive figured out the solution for the differential equation to be, S = ce^kt - D/k

If somebody invest 20,000 each year for the next 40 years with continuous compounded growth of 2%, the final value should be about 1,237,837.

I don't see how the equation S = ce^kt - D/k works to 1,237,837.

I plug c = 20,000, k = .02, t = 40, and D = 20,000 and I get S = -955489

What am I doing wrong?

 

[Dick]

'c' isn't 20000. The 20000 is D, which is your rate of savings. You have to work out what 'c' is by setting S(0) to be what your initial savings is. It's a boundary value problem.