#!/bin/bash
# monthlypmt.sh: Calculates monthly payment on a mortgage.
# This is a modification of code in the "mcalc" (mortgage calculator) package,
#+ by Jeff Schmidt and Mendel Cooper (yours truly, the author of this document).
# http://www.ibiblio.org/pub/Linux/apps/financial/mcalc-1.6.tar.gz [15k]
echo
echo "Given the principal, interest rate, and term of a mortgage,"
echo "calculate the monthly payment."
bottom=1.0
echo
echo -n "Enter principal (no commas) "
read principal
echo -n "Enter interest rate (percent) " # If 12%, enter "12", not ".12".
read interest_r
echo -n "Enter term (months) "
read term
interest_r=$(echo "scale=9; $interest_r/100.0" | bc) # Convert to decimal.
# "scale" determines how many decimal places.
interest_rate=$(echo "scale=9; $interest_r/12 + 1.0" | bc)
top=$(echo "scale=9; $principal*$interest_rate^$term" | bc)
echo; echo "Please be patient. This may take a while."
let "months = $term - 1"
# ====================================================================
for ((x=$months; x > 0; x--))
do
bot=$(echo "scale=9; $interest_rate^$x" | bc)
bottom=$(echo "scale=9; $bottom+$bot" | bc)
# bottom = $(($bottom + $bot"))
done
# ====================================================================
# --------------------------------------------------------------------
# Rick Boivie pointed out a more efficient implementation
#+ of the above loop, which decreases computation time by 2/3.
# for ((x=1; x <= $months; x++))
# do
# bottom=$(echo "scale=9; $bottom * $interest_rate + 1" | bc)
# done
# And then he came up with an even more efficient alternative,
#+ one that cuts down the run time by about 95%!
# bottom=`{
# echo "scale=9; bottom=$bottom; interest_rate=$interest_rate"
# for ((x=1; x <= $months; x++))
# do
# echo 'bottom = bottom * interest_rate + 1'
# done
# echo 'bottom'
# } | bc` # Embeds a 'for loop' within command substitution.
# --------------------------------------------------------------------------
# On the other hand, Frank Wang suggests:
# bottom=$(echo "scale=9; ($interest_rate^$term-1)/($interest_rate-1)" | bc)
# Because . . .
# The algorithm behind the loop
#+ is actually a sum of geometric proportion series.
# The sum formula is e0(1-q^n)/(1-q),
#+ where e0 is the first element and q=e(n+1)/e(n)
#+ and n is the number of elements.
# --------------------------------------------------------------------------
# let "payment = $top/$bottom"
payment=$(echo "scale=2; $top/$bottom" | bc)
# Use two decimal places for dollars and cents.
echo
echo "monthly payment = \$$payment" # Echo a dollar sign in front of amount.
echo
exit 0
# Exercises:
# 1) Filter input to permit commas in principal amount.
# 2) Filter input to permit interest to be entered as percent or decimal.
# 3) If you are really ambitious,
# expand this script to print complete amortization tables.