Hi there,
I'm extremely new to Mathematica. I am trying to build a loan model wherein I use a first order difference equation to create a spreadsheet based on parameters I set in the equation. I have a few specific questions in mind...
Since I know Latex, I'm going to present my equation in that format. I'm using the following system of equations: $x_{n+1}=\lambda x_{n} + b_{n+1}, b_{n+1}=\alpha b_{n}$ is the specific system, where $\lambda=1+r$, and $0<r<1$ is an interest rate on the loan $x_{n}$ given the n^th month on the loan from month $n=0$. Moreover, $\alpha\geq 1, x_{0}=5000,b_{0}=439.79$. For the sake of a table and/or graph of data based on the solved equation (which I know to be $x_{n}=\lambda^{n}x_{0}-b_{0}\sum_{i=1}^{n}\alpha^{i}\lambda^{n-i}$. I can solve the equation perfectly fine and I understand finite difference equations and discrete dynamical systems, but I have zero clue when it comes to Mathematica's syntax, formatting, etc. Please help! This is the pathetic start on things I have right now:
Rsolve[{x[1 + n] == b[1 + n] + \[Lambda]x[n],
b[1 + n] == \[Alpha]b[n], \[Lambda] == 1 + r,
0 < r < 1, \[Alpha] >= 1, x[0] == 5000, b[0] == 438.79}, {x[1 + n],
b[1 + n]}, 360 >= n >= 0]
I would ideally like to create something where I have knobs to adjust the parameters lambda (or r, alternatively) and alpha, with a corresponding plot that will shift in accordance to how the parameters are tweaked. Finally, I'd like to be able to create a table of values or spreadsheet for payment amount $b_{n}$ over varying alpha values. Let me know if you have tips, tricks, answers, or resources that can get me on my way!