#!/usr/bin/Rscript
# Copyright © 2017 Martin Ueding <mu@martin-ueding.de>

###############################################################################
#                          Parameters of the Problem                          #
###############################################################################

# Cashback that the insurance company offers.
cashback <- 0.04

# Interest that can be gained with long-term investments.
interest.long <- 0.06

# Short-term interest rate.
interest.short <- 0.01

# Yearly rate without cashback.
monthly.rate <- 33.78

annual.payments <- 1

###############################################################################
#                               Implementation                                #
###############################################################################

# Say that the insurance start on January 1st. Month 0 is the December of the
# preceding year, month 1 is the first January. This is counted at the
# beginning of the month after all transactions have taken place.
month <- c(0:60)

year <- floor(month / 12)
december <- which(month %% 12 == 0)

# Initially we have 11 monthly rates extra money. In January, we just got new
# salary which will be used in part to pay the insurance.
savings.initial <- 11 * monthly.rate

###############################################################################
#                            Model A: No cashbash                             #
###############################################################################

A <- data.frame(month=month)

# All extra money is put into the portfolio. Assuming that the interest is
# stable, we can compute the amount of money in the portfolio at each beginning
# of the months. Since the money is put in it in January, there is no interest
# in January.
A$portfolio.value <- savings.initial * (1 + interest.long)^((month-1)/12)

# The total amount of money that we have payed to the insurance company is just
# the accumulation of the monthly rates. In January we will have payed the
# first rate.
A$payed <- month * monthly.rate

A$cost <- A$portfolio.value - savings.initial

###############################################################################
#                              Model B: Cashback                              #
###############################################################################

B <- data.frame(month=month)

B$payed <- vector(length=length(month))
B$savings <- vector(length=length(month))

# In December, we have not payed anything and have everything in the savings
# account.
B$payed[1] <- 0
B$savings[1] <- savings.initial

# For the next months, we need to compute what happens. Note that `i == 2`
# corresponds to January because arrays in R are 1-indexed. The loop therefore
# starts with January.
for (i in c(2:61)) {
    # First the balances of the previous month are copied to this month.
    B$payed[i] <- B$payed[i-1]
    B$savings[i] <- B$savings[i-1]

    # On the savings account we have gotten interest for the preceding month.
    if (month[i] >= 2) {
        B$savings[i] <- B$savings[i] * (1 + interest.short)^(1/12)
    }

    # Then we get salary this month which gets added to our savings account.
    B$savings[i] <- B$savings[i] + monthly.rate
    B$payed[i] <- B$payed[i] + monthly.rate

    # If it is a January, we need to pay the insurance.
    if (month[i] %% 12 == 1 || (annual.payments == 2 && month[i] %% 12 == 7)) {
        # We have to pay the whole year in advance, but we get a cashback.
        # Transfer the money from the savings account to the insurance company.
        transfer <- 12 / annual.payments * monthly.rate * (1 - cashback / annual.payments)
        B$savings[i] <- B$savings[i] - transfer
    }
}

B$cost <- B$savings - savings.initial

###############################################################################
#                                    Plots                                    #
###############################################################################

# Useful plots.

svg('payed.svg')
plot(month, A$payed, type='s', main='Money payed to insurer', xlab='Month',
     ylab='EUR', col='blue', ylim=range(A$payed, B$payed))
lines(month, B$payed, type='s', col='red')
dev.off()

svg('savings.svg')
x <- month
y1 <- A$portfolio.value
y2 <- B$savings
plot(x, y1, type='s', main='Money in portfolio/savings',
     xlab='Month', ylab='EUR', col='blue',
     ylim=range(y1, y2))
lines(x, y2, type='s', col='red')
dev.off()

svg('cost.svg')
x <- year[december][2:length(year[december])]
y1 <- diff(A$cost[december])
y2 <- diff(B$cost[december])
plot(x, y1,
     type='p', main='Financial advantage each year',
     xlab='Year', ylab='EUR', col='blue',
     ylim=range(y1, y2))
points(x, y2, col='red')
dev.off()

print(diff(A$cost[december]))
print(diff(B$cost[december]))

plot(year[december], (A$cost[december] - B$cost[december]) / year[december])

# Elementary plots.

#plot(month, A$payed)
#plot(month, A$portfolio.value)
#plot(year[december], A$cost[december])

#plot(month, B$payed)
#plot(month, B$savings)
#plot(year[december], B$cost[december])

cost.A <- A$cost[length(A$cost)]
cost.B <- B$cost[length(B$cost)]

print(cost.A)
print(cost.B)
print(cost.A - cost.B)
print(1 - cost.B / cost.A)