#!/bin/sh

#  mortgage - given a principal loan amount, interest rate, and 
#    duration of loan (years), calculate the per-payment amount.

# formula is:    M = P * ( J / (1 - (1 + J) ** -N))
#    where P = principal, J = monthly interest rate, N = duration (months)
#
# users typically enter P, I (annual interest rate) and L (length, years)

. 012-library.sh

if [ $# -ne 3 ] ; then
  echo "Usage: $0 principal interest loan-duration-years" >&2
  exit 1
fi

P=$1  I=$2   L=$3
J="$(scriptbc -p 8 $I / \( 12 \* 100 \) )"
N="$(( $L * 12 ))"
M="$(scriptbc -p 8 $P \* \( $J / \(1 - \(1 + $J\) \^ -$N\) \) )"

# now a little prettying up of the value:

dollars="$(echo $M | cut -d. -f1)"
cents="$(echo $M | cut -d. -f2 | cut -c1-2)"

cat << EOF
A $L year loan at $I% interest with a principal amount of $(nicenumber $P 1 ) 
results in a payment of \$$dollars.$cents each month for the duration of
the loan ($N payments).
EOF

exit 0