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## Function to Calculate Monthly Mortgage Payments and Amortization Tables ##
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# Author: Thomas Girke
# Last update: Feb 27, 2007
# Utility: Calculates monthly and annual loan or mortgage payments, generates amortization tables and plots the results
# How to run the script:
# source("http://faculty.ucr.edu/~tgirke/Documents/R_BioCond/My_R_Scripts/mortgage.R")

# Definitions: 
#   P = principal, the initial amount of the loan
#   I = annual interest rate
#   L = length of the loan in years, or at least the length over which the loan is amortized.
#   J = monthly interest in decimal form = I / (12 x 100)
#   M = monthly payment; formula: M = P * ( J / (1 - (1 + J) ^ -N))
#   N = number of months over which loan is amortized = L x 12
# see also: http://www.jeacle.ie/mortgage/instructions.html


source("~/Dropbox/dev/R/!ScriptsR/basicWrappers.r")

loan <- function(P=500000, intrPercent=6, years=30, monthsWithOutPayments=0, amort=TRUE, plotData=FALSE) { 
  # monthsWithOutPayments, used for student loans.  Interest acrues, compounded monthly.  
  # time for Amortization begins after that
  cat("\n\n")
  I <- intrPercent
  L <- years #for ease of notation
  J <- I/(12 * 100)
  P <- P * ((1+J) ^ monthsWithOutPayments)  # for student loans
  cat("Principal when amortization begins is: ", asCurr(P), "\n")
  N <- 12 * L
  M <- P*J/(1-(1+J)^(-N))
  monthPay <<- M
  cat("\nThe payments for this loan are:\n 
      Monthly payment: ", asCurr(M), " (stored in monthPay)\n
      Total cost: ", asCurr(M*N), "\n\n", sep="")

  # Calculate Amortization for each Month
  if(amort) {
    Pt <- P # current principal or amount of the loan
    currP <- NULL  # vector tracking Principal after each payment 
    while(Pt>=0) {
      H <- Pt * J # this is the current monthly interest
      C <- M - H # this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for that month
      Pt <- Pt - C # this is the new balance of your principal of your loan
      currP <- c(currP, Pt)
    } # The loop continues until the value Q (and hence P) goes to zero
     
    monthP <- c(P, currP[1:(length(currP)-1)])-currP
    aDFmonth <<- data.frame(
                Amortization=c(P, currP[1:(length(currP)-1)]), 
                Monthly_Payment=monthP+c((monthPay-monthP)[1:(length(monthP)-1)],0),
                Monthly_Principal=monthP, 
                Monthly_Interest=c((monthPay-monthP)[1:(length(monthP)-1)],0), 
                Year=sort(rep(1:ceiling(N/12), 12))[1:length(monthP)]
        )
    aDFyear <- data.frame(
               Amortization=tapply(aDFmonth$Amortization, aDFmonth$Year, max), 
               Annual_Payment=tapply(aDFmonth$Monthly_Payment, aDFmonth$Year, sum), 
               Annual_Principal=tapply(aDFmonth$Monthly_Principal, aDFmonth$Year, sum), 
               Annual_Interest=tapply(aDFmonth$Monthly_Interest, aDFmonth$Year, sum), 
               Year=as.vector(na.omit(unique(aDFmonth$Year)))
               )
    aDFyear <<- aDFyear
    cat("The amortization data for each of the", N, "months are stored in \"aDFmonth\".\n\n")
    cat("The amortization data for each of the", L, "years are stored in \"aDFyear\".\n\n")
  }

  if(plotData) {
  barplot(t(aDFyear[,c(3,4)]), 
    col=c("blue", "red"), 
    main="Annual Interest and Principal Payments", 
    sub="The data for this plot is stored in aDFyear.",
    xlab="Years", ylab="$ Amount", 
    legend.text=c("Principal", "Interest"), 
    ylim=c(0, max(aDFyear$Annual_Payment)*1.3))
  }
}



cat("The monthly loan payments and amortization rates can be calculted with the loan() function like this: \n 
  loan(P=500000, I=6, L=30, amort=T, plotData=T)
    P = principal (loan amount)
    I = annual interest rate
    L = length of the loan in years \n")