##
## Get the function spot_rates_to_discount_factors:
##
source('dup_table_4_2.R')

##
## Get the spot rates:
##
source('exercise_2.R')

##
## Part (a):
##
dk = spot_rates_to_discount_factors(s)
dk = c(1, dk)
print(round(dk, 3))

x = c(-40, rep(10, 6)) ## the cash flow
PV = sum( dk * x )
print(sprintf('PV (dicount method)= %f', PV))

##
## Part (b):
##
ndk = length(dk)
dk_n_kp1 = c( dk[ndk] / dk[ndk-1] )
ndk = ndk - 1
while( ndk > 0 ){
    dk_n_kp1 = c( dk[ndk] / dk[ndk-1], dk_n_kp1 )
    ndk = ndk - 1
}

print('d_{k, k+1}=')
print(dk_n_kp1)

nx = length(x)
PV = x[nx]
k = nx-1
while(k > 0){
    PV = x[k] + dk_n_kp1[k] * PV
    k = k-1
}
print(sprintf('PV (running method)= %f', PV))