[PYTHON] What is equal repayment of principal and interest and equal repayment of principal and interest?

There are two ways to repay a mortgage. Even when I read the book, I felt uncomfortable with only the figures that I could not understand, so I tried to express it with mathematical formulas.

Reference example that I personally found difficult to understand

http://www.flat35.com/faq/faq_208-4.html

What is equal repayment of principal and interest?

It is a repayment method in which "fixing the monthly repayment amount" is given top priority, and the amount obtained by subtracting interest from it is used for the principal.

months = range(0, 35 * 12)
residual =  36000000
r = 0.012
fixed = 120000

hist_residual = []
hist_reduction = []
hist_interst = []
hist_month = []

for month in months:
    if residual < 0: break
    reduction = fixed - residual * r / 12.0
    residual = residual - reduction
    
    hist_month.append(month)
    hist_residual.append(residual)
    hist_reduction.append(reduction)
    hist_interst.append(residual * r / 12.0)
    
fig, axs = plt.subplots(2, sharex=True)
axs[0].plot(hist_month, hist_residual)
axs[0].set_ylabel('residual')
axs[1].stackplot(hist_month, [hist_reduction, hist_interst], colors=['blue', 'pink'], labels=['residual', 'interest'])
axs[1].set_xlabel('month')
axs[1].legend()

What is equal principal repayment?

A method in which the highest priority is to "reduce the principal by a fixed amount every month" and the amount obtained by adding interest to that amount is used as the monthly repayment amount.

months = range(0, 35 * 12)
residual =  36000000
r = 0.012
fixed = 100000

hist_residual = []
hist_reduction = []
hist_interst = []
hist_month = []

for month in months:
    if residual < 0: break
    reduction = fixed 
    residual = residual - fixed
    
    hist_month.append(month)
    hist_residual.append(residual)
    hist_reduction.append(reduction)
    hist_interst.append(residual * r / 12.0)
    
fig, axs = plt.subplots(2, sharex=True)
axs[0].plot(hist_month, hist_residual)
axs[0].set_ylabel('residual')
axs[1].stackplot(hist_month, [hist_reduction, hist_interst], colors=['blue', 'pink'], labels=['residual', 'interest'])
axs[1].set_xlabel('month')
axs[1].legend()

Impressions

I thought that miscommunication would be reduced if it was written in a calculation formula / programming language rather than expressed in letters because it would be transmitted without error.