#############################################################################
## Function to Calculate Monthly Mortgage Payments and Amortization Tables ##
#############################################################################
# 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

mortgage <- function(P=500000, I=6, L=30, plotData=TRUE) { 
    J <- I/(12 * 100)
    N <- 12 * L
    M <- P*J/(1-(1+J)^(-N))
    monthPay <- M
    cat("\nThe payments for this loan are:\n 
            Monthly payment: $", M, " (stored in m$monthPay)\n
            Total cost: $", M*N, "\n\n", sep="")
    # Calculate Amortization for each Month
    Pt <- P # current principal or amount of the loan
    currP <- NULL
    while(Pt>=0) {
        H <- Pt * J # this is the current monthly interest
        C <- M - H # this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for that month
        Q <- Pt - C # this is the new balance of your principal of your loan
        Pt <- Q # sets P equal to Q and goes back to step 1. The loop continues until the value Q (and hence P) goes to zero
        currP <- c(currP, Pt)
    }
    monthP <- c(P, currP[1:(length(currP)-1)])-currP
    aDFmonth <- data.frame(
                      Amortization=c(P, currP[1:(length(currP)-1)]), 
                      Monthly_Payment=monthP+c((monthPay-monthP)[1:(length(monthP)-1)],0),
                      Monthly_Principal=monthP, 
                      Monthly_Interest=c((monthPay-monthP)[1:(length(monthP)-1)],0), 
                      Year=sort(rep(1:ceiling(N/12), 12))[1:length(monthP)]
            )
    aDFyear <- data.frame(
                     Amortization=tapply(aDFmonth$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 \"m$aDFmonth\".\n\n")
    cat("The amortization data for each of the", L, "years are stored in \"m$aDFyear\".\n\n")
    # Plot amortization results
    if(plotData==TRUE) {
    barplot(t(aDFyear[,c(3,4)]), 
        col=c("#00BFC4", "#F8766D"), 
        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))
    }
    return(list(monthPay=monthPay, aDFmonth=aDFmonth, aDFyear=aDFyear))
}
cat("The monthly mortgage payments and amortization rates can be calculted with the mortgage() function like this: \n 
    m <- mortgage(P=500000, I=6, L=30, plotData=TRUE)
        P = principal (loan amount)
        I = annual interest rate
        L = length of the loan in years \n")