Fun with mortgage amortizations

amortization.R

#	Credit due to Thomas Girke ("http://faculty.ucr.edu/~tgirke/Documents/R_BioCond/My_R_Scripts/mortgage.R") for original implementation of mortgage()
# 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.

# to use, run it as graphs <- amortizationScenarios(P, I, L), then graphs[1], graphs[2]


amortizationScenarios <- function(P=500000, I = 6, L=30) {
  library(ggplot2)
  mortgage <- function(P=500000, I=6, L=30, extra = 0) { 
  	J <- I/(12 * 100)
  	N <- 12 * L
  	M <- (P*J/(1-(1+J)^(-N))) * (1 + extra/12)
  	monthPay <<- M
  	# 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
  }

  alternatives = list()
  extraInterest <- c()
  amortizationCurves <- data.frame(stringsAsFactors=F)
  
  for(extra in 0:12) {
    mortgage(P, I, L, extra)
    alternatives[[extra+1]] <- aDFmonth
    cat("With", extra, "payments per year:\n")
    cat("Average monthly payment over life of loan: ", mean(aDFmonth$Monthly_Payment), "\n")
    cat("Months to payoff: ", nrow(aDFmonth), "\n")    
    cat("Total payment vs. original principal:", sum(aDFmonth$Monthly_Payment)/aDFmonth$Amortization[1], "\n\n\n\n")
    extraInterest[extra+1] <- sum(aDFmonth$Monthly_Payment)/aDFmonth$Amortization[1]

    amortizationCurves <- rbind(amortizationCurves, data.frame(extra = extra, month = as.numeric(row.names(aDFmonth)), principal = aDFmonth$Amortization, stringsAsFactors=F))
  }
  
  a <- ggplot(data.frame(extraPayments=0:12, premium = extraInterest), aes(x=extraPayments, y=premium, group=1)) + geom_line(colour='steelblue', size=I(2)) + opts(title="Total amount paid relative to original principal") + ylab("Total payments relative to original loan amount") + xlab("Number of extra payments made annually")

 b <- ggplot(amortizationCurves, aes(x=month, y=principal, group = extra)) + geom_line(aes(colour=extra)) + xlab("Months since origination") + ylab("Principal outstanding") + opts(title="Mortgage payoff relative to extra payments made") + scale_colour_continuous(name="Number of extra payments") 

 return(list(a,b))
}