#!/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 + $bot")) done # ==================================================================== # -------------------------------------------------------------------- # Rick Boivie pointed out a more efficient implementation #+ of the above loop, which decreases computation time by 2/3. # for ((x=1; x # do # bottom=$(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=$interest_rate" # for ((x=1; x # do # echo 'bottom = bottom * interest_rate + 1' # done # echo 'bottom' # } | bc` # Embeds a 'for loop' within command substitution. # -------------------------------------------------------------------------- # On the other hand, Frank Wang suggests: # bottom=$(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.
