## The first mortgage:
##
rate = 0.07625
pts = 0.01
term = 30
MA = 203150.00
APR = 0.07883

n = 12*term
r = APR/12
A = ( r * (1+r)^n * MA ) / ( (1+r)^n - 1 )

r = rate/12
P = (A/r) * (1 - 1/(1+r)^n )

fees_N_expenses = P - MA
fee = MA * pts
expenses = fees_N_expenses - fee
print(sprintf('A= %.2f; P(rate)= %.2f; fees_N_expenses= %.2f; fee= %.2f; expenses= %.2f', A, P, fees_N_expenses, fee, expenses)) ## these matches the sumber given in Example 3.3 (APR)


## The second mortgage:
##
rate = 0.07875
pts = 0.005
term = 30
MA = 203150.00
APR = 0.08083

n = 12*term
r = APR/12
A = ( r*(1+r)^n * MA)/((1+r)^n - 1)

r = rate/12
P = (A/r) * (1 - 1/(1+r)^n)

fees_N_expenses = P - MA
fee = MA * pts
expenses = fees_N_expenses - fee
print(sprintf('A= %.2f; P(rate)= %.2f; fees_N_expenses= %.2f; fee= %.2f; expenses= %.2f', A, P, fees_N_expenses, fee, expenses))