P = 100000.00
rate = 0.1
term = 30

## Under monthly payments:
##
n = 12*term
r = rate/12
x = ( r * (1+r)^n * P )/( (1+r)^n - 1 )
total_payed = n*x
interest_payed_montly = total_payed - P
print(sprintf('Monthy: x= %.2f; total_payed= %.2f; interest_payed= %.2f', x, total_payed, interest_payed_montly) )

## Under biwekly payments:
##
r = rate/26
A = x/2 # what we pay every two weeks
root_fn = function(y){
    n = 26*y
    err = P - (A/r) * (1 - 1/(1+r)^n )
    return(err)
}

## Lets get an idea about how many years till be pay off the loan:
##
y = seq(18, 24, length.out=20)
plot(y, root_fn(y), type='l')
abline(h=0, col='blue')
grid()


## Find the value of y the loan is payed off:
##
source('http://waxworksmath.com/Authors/A_F/Conte/Code/Chapter3/utils.R')
##source('../../../../Conte/Code/Chapter3/utils.R")
rt = bisection_method(18, 24, root_fn)
print(rt)

y = rt[1] # number of years
n = round(26*y) # number of biweekly payments
total_payed = n*x/2
interest_payed_biweekly = total_payed - P
print(sprintf('Biweekly: years_till_payed= %.3f; n_payments= %.1f', y, n))
print(sprintf('Biweekly: x/2= %.2f; total_payed= %.2f; interest_payed= %.2f', x/2, total_payed, interest_payed_biweekly))

savings_in_interest = interest_payed_montly - interest_payed_biweekly
print(sprintf('Interest Savings of Biweekly over Monthly= %.2f', savings_in_interest))