Say you put 10,000 into a saving account which has a 3% APR (left alone, the account increases by 3% each year). Assume you withdraw $20 a month from this account to pay for your gym membership, but otherwise leave it alone to accrue interest.
(a) Craft a differential equation which modeling this situation.
(b) Find the general solution for the differential equation in (a).
(c) Use the given initial condition to find a particular solution to the differential equation in (a).
I really only need help with part a, I'm completely fine with actually finding the solutions to differential equations once I have them. I'm just unsure how to start this one.
The question mentions that it increase 3% each year left alone so I'm thinking that means compounding isn't required, I wouldn't know what to do then. So I don't know if I can just have the percent increase and manual withdrawals happening at the same time.
The starting equation I came up with was dP/dt = 0.03P - 240 to relate the two quantities, I'm unsure of this and would appreciate help.
That differential equation you came up with is exactly correct. Don't worry about compounding, that only starts to be a headache when dealing with difference equations.