Implementing difference (NOT differential) equations in Python

Question

I'm trying to implement a difference equation in Python. These take the form y_n+1 = a * y_n + b, given y₀ where y₀ is initial value and it iterates -- meaning

y₁ = a * y₀ + b,
y₂ = a * y₁ + b,
...

An example problem (from my calculus class) would be thus: Say you take out a loan of $60,000 and plan on paying $700 a month back at an interest rate of 1.2%. How much would be left after 5 years? This would be set up as y_n+1 = 1.1 * y_n - 700, y₀ = 60,000

I understand recursion in Python in the sense that you can say, for example,

i = 0
while i < 20:
    i = i+1

but I'm unsure how to approach it when the next iteration requires a value from the previous.

Answer 1

Typically you'd do this by storing a single variable with the last value from the calculation, and seeding it with your starting value. EG:

y = 60000
while True:
    y = .1 * y - 700

Of course, you have to determine when to stop and what to do with the values. You certainly want to print them:

y = 60000
while True:
    y = .1 * y - 700
    print(y)

But you probably only want to do it for 100 times or something instead of forever:

y = 60000
for i in range(12*5):
    y = .1 * y - 700
    print("%d: %f" % (i,y))

And you may want to store them for use later as well, so put those in an array:

y = 60000
results=[]
for i in range(12*5):
    y = .1 * y - 700
    results.append(y)

print(results)