#==============================================
# Figure 2.1.R.
# R script to calculate and plot
# monthly loan payment information.
#==============================================

#----------------------------------------------
# Step 0.  Assign numerical values to P (principal), m
# (total number of monthly payments), and i (annual interest
# rate).  Calculate s (monthly interest rate).
#----------------------------------------------
P=25000
m=360
i=.05    # Interest is 100*i percent per year.
s=i/12   # Monthly interest rate.

#----------------------------------------------
# Step 1.  Calculate a vector of values of time (months) going
# from 1 to m.
#----------------------------------------------
t=1:m

#----------------------------------------------
# Step 2.  Calculate the monthly payment (a single number) using
# the first loan equation.
#----------------------------------------------
monthly.payment=(1+s)^m*s*P/((1+s)^m-1)

#----------------------------------------------
# Step 3.  Calculate a vector of principal amounts paid each
# month of the loan using the second loan equation.
#----------------------------------------------
principal.paid.month.t=(1+s)^(t-1)*s*P/((1+s)^m-1)

#----------------------------------------------
# Step 4.  Calculate a vector of principal amounts remaining
# unpaid each month of the loan using the third loan equation.
#----------------------------------------------
principal.remaining=P*(1-((1+s)^t-1)/((1+s)^m-1))

#----------------------------------------------
# Step 5.  Calculate a vector of the interest amounts paid each
# month by subtracting the principal amounts paid from the
# monthly payment.
#----------------------------------------------
interest.paid.month.t=monthly.payment-principal.paid.month.t

#----------------------------------------------
# Step 6.  Calculate the total interest paid by summing all the
# interest amounts paid each month using the sum( ) function
# in R.
#----------------------------------------------
total.interest.paid=sum(interest.paid.month.t)

#----------------------------------------------
# Step 7.  Print the results to the console.
#----------------------------------------------
monthly.payment
total.interest.paid
t
principal.paid.month.t
interest.paid.month.t
principal.remaining

#----------------------------------------------
# Step 8.  Draw a graph of the principal remaining in the loan
# each month (vertical axis) versus the vector of months
# (horizontal axis).
#----------------------------------------------
plot(t,principal.remaining,type="l")