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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 16: True Discount"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.1, Page number 16.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "present worth is 160.0 Rs\n",
+ "true discount is 16.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=176; #principal(Rs)\n",
+ "R=6; #rate(%)\n",
+ "T=20/12; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "PW=P/(1+(R*T/100)); #present worth(Rs)\n",
+ "TD=P-PW; #true discount(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"present worth is\",PW,\"Rs\"\n",
+ "print \"true discount is\",TD,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.2, Page number 16.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "present worth is 2000.0 Rs\n",
+ "true discount is 420.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=2420; #principal(Rs)\n",
+ "R=10; #rate(%)\n",
+ "T=2; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "PW=P/((1+(R/100))**T); #present worth(Rs)\n",
+ "TD=P-PW; #true discount(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"present worth is\",PW,\"Rs\"\n",
+ "print \"true discount is\",TD,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.3, Page number 16.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "present worth is 3000.0 Rs\n",
+ "amount of the bill is 3240.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=12; #rate(%)\n",
+ "T=8/12; #time(yrs)\n",
+ "TD=240; #true discount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "PW=100*TD/(R*T); #present worth(Rs)\n",
+ "P=PW+TD; #amount of the bill(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"present worth is\",PW,\"Rs\"\n",
+ "print \"amount of the bill is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.4, Page number 16.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "difference between simple interest and true discount is 32.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=960; #principal(Rs)\n",
+ "R=5; #rate(%)\n",
+ "T=4; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "SI_TD=(P*(R*T)**2)/(100*(100+(R*T))); #difference between simple interest and true discount(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"difference between simple interest and true discount is\",SI_TD,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.5, Page number 16.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "principal is 38250.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=4; #rate(%)\n",
+ "T=6/12; #time(yrs)\n",
+ "SI_TD=15; #difference between simple interest and true discount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "P=SI_TD*100*(100+(R*T))/((R*T)**2); #principal(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"principal is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.6, Page number 16.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time is 4.0 months\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=2040; #principal(Rs)\n",
+ "R=6; #rate(%)\n",
+ "TD=40; #true discount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "T=100*TD/(R*(P-TD)); #time(yrs)\n",
+ "\n",
+ "#Result\n",
+ "print \"time is\",T*12,\"months\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.7, Page number 16.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate is 1.11 %\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=1860; #principal(Rs)\n",
+ "T=3; #time(yrs)\n",
+ "TD=60; #true discount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "R=100*TD/(T*(P-TD)); #rate(%) \n",
+ "\n",
+ "#Result\n",
+ "print \"rate is\",round(R,2),\"%\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.8, Page number 16.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "amount of the bill is 1575.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=5/12; #time(yrs)\n",
+ "TD=75; #true discount(Rs)\n",
+ "R=12; #rate(%)\n",
+ "\n",
+ "#Calculation\n",
+ "P=TD*(1+(100/(R*T))); #amount of the bill(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"amount of the bill is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.9, Page number 16.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sum is 600.0 Rs\n",
+ "rate per annum is 16.67 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "TD=200; #true discount(Rs)\n",
+ "SI=300; #simple interest(Rs)\n",
+ "T=3; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "P=SI*TD/(SI-TD); #sum(Rs)\n",
+ "R=100*SI/(P*T); #rate per annum(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"sum is\",P,\"Rs\"\n",
+ "print \"rate per annum is\",round(R,2),\"%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.10, Page number 16.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "true discount is 96.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "TD1=60; #true discount(Rs)\n",
+ "T1=1; #assume\n",
+ "T2=2*T1;\n",
+ "R1=R2=1; #assume\n",
+ "P=240; #sum(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=(P-TD1)/(T2*TD1);\n",
+ "TD2=P/(x+1); #true discount(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"true discount is\",TD2,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.11, Page number 16.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate percent is 18.18 %\n",
+ "sum of the bill is 1636.36 Rs\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "PW1=1500; #present worth(Rs)\n",
+ "PW2=1200; #present worth(Rs)\n",
+ "T1=6/12; #time(yrs)\n",
+ "T2=2; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=PW1/PW2;\n",
+ "R=100*(x-1)/(T2-(x*T1)); #rate percent(%)\n",
+ "P=PW1*(1+(R*T1/100)); #sum of the bill(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate percent is\",round(R,2),\"%\"\n",
+ "print \"sum of the bill is\",round(P,2),\"Rs\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.12, Page number 16.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate percent is 4.0 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P1=600; #sum(Rs)\n",
+ "P2=720; #sum(Rs)\n",
+ "T=5; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "R=((P2*T*100/(P1*T))-100)/T; #rate percent(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate percent is\",R,\"%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 16.13, Page number 16.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "each installment should be 2000.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=8480; #sum(Rs)\n",
+ "n=4; #number of installments\n",
+ "r=16; #rate percent(%)\n",
+ "y=4;\n",
+ "\n",
+ "#Calculation\n",
+ "x=r*n*(n-1)/(100*y*2);\n",
+ "a=P/(x+n); #each installment should be(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"each installment should be\",a,\"Rs\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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