source('./utils.R')


## Part (a):
##
P = 100000
n = 30
r = 0.08

A = annuity_payment(P, n, r)
print(A)


## Part (b):
##
current_debt = c(P)
n= 5
for( yi in seq(1, n) ){
    lcdi = length(current_debt)
    debt_plus_interest = current_debt[lcdi] * (1+r)
    current_debt = c(current_debt, debt_plus_interest-A)
}
print('current_debt=')
print(current_debt)

## Part (c):
##
lcdi = length(current_debt)
P_now = current_debt[lcdi] # the amount still to be paid
r = 0.09
n = 25
A_prime = annuity_payment(P_now, n, r)
print(A_prime)


## Part (d):
##
root_fn = function(n, P, A, r){
    err = P - annuity_PV(A, n, r)
    return(err)
}

## Lets get an idea about how many more years are needed untill we pay off the loan:
##
ns = seq(35, 40, length.out=20)
plot(ns, root_fn(ns, P_now, A, r), type='l', xlab='n')
abline(h=0, col='blue')
grid()
source('http://waxworksmath.com/Authors/A_F/Conte/Code/Chapter3/utils.R')
##source('../../../../Conte/Code/Chapter3/utils.R')

rt = bisection_method(35, 40, function(x) {root_fn(x, P_now, A, r)})
print(rt)

n = rt[1] # number of years needed to payoff the new loan
print(sprintf('years_till_payed= %.3f', n))