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diff --git a/Quantitative_Aptitude_for_Competitive_Examinations/Chapter15.ipynb b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter15.ipynb new file mode 100755 index 00000000..1809068a --- /dev/null +++ b/Quantitative_Aptitude_for_Competitive_Examinations/Chapter15.ipynb @@ -0,0 +1,704 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 15: Compound Interest"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.1, Page number 15.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "amount is 4410.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=4000; #principal(Rs)\n",
+ "R=5; #rate(%)\n",
+ "T=2; #time(yrs)\n",
+ "n=1;\n",
+ "\n",
+ "#Calculation\n",
+ "A=P*(1+(R/(100*n)))**(n*T); #amount(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"amount is\",A,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.2, Page number 15.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "compound interest is 662.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=2000; #principal(Rs)\n",
+ "R=10; #rate(%)\n",
+ "T=3; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=R/100;\n",
+ "y=(1+x)**T;\n",
+ "CI=P*(y-1); #compound interest(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"compound interest is\",CI,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.3, Page number 15.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "principal is 800.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=10; #rate(%)\n",
+ "T=2; #time(yrs)\n",
+ "A=968; #amount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "P=A/(1+(R/100))**T; #principal(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"principal is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.4, Page number 15.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "compound interest is 4921.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=64000; #principal(Rs)\n",
+ "R=2.5; #rate(%)\n",
+ "T=3; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=R/100;\n",
+ "y=(1+x)**T;\n",
+ "CI=P*(y-1); #compound interest(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"compound interest is\",CI,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.5, Page number 15.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "compound interest in 1st case is 122 Rs\n",
+ "compound interest in 2nd case is 121.2 Rs\n",
+ "answer given in the book is wrong\n",
+ "compound interest in 3rd case is 119.0 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",
+ "P=2000; #principal(Rs)\n",
+ "R=8; #rate(%)\n",
+ "T=9/12; #time(yrs)\n",
+ "n1=4;\n",
+ "n2=2;\n",
+ "n3=1;\n",
+ "\n",
+ "#Calculation\n",
+ "A1=P*(1+(R/(100*n1)))**(n1*T); #amount(Rs)\n",
+ "CI1=A1-P; #compound interest in 1st case(Rs)\n",
+ "A2=P*(1+(R/(100*n2)))**(n2*T); #amount(Rs)\n",
+ "CI2=A2-P; #compound interest in 2nd case(Rs)\n",
+ "A3=P*(1+(R/(100*n3)))**(n3*T); #amount(Rs)\n",
+ "CI3=A3-P; #compound interest in 3rd case(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"compound interest in 1st case is\",int(CI1),\"Rs\"\n",
+ "print \"compound interest in 2nd case is\",round(CI2,1),\"Rs\"\n",
+ "print \"answer given in the book is wrong\"\n",
+ "print \"compound interest in 3rd case is\",round(CI3),\"Rs\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.6, Page number 15.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sum is 31250.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=4; #rate(%)\n",
+ "T=2; #time(yrs)\n",
+ "CI_SI=50; #difference between CI and SI(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=(R/100)**2;\n",
+ "P=CI_SI/x; #sum(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"sum is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.7, Page number 15.6"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "difference between CI and SI is 20.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=10; #rate(%)\n",
+ "T=2; #time(yrs)\n",
+ "P=2000; #sum(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=(R/100)**2;\n",
+ "CI_SI=P*x; #difference between CI and SI(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"difference between CI and SI is\",CI_SI,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.8, Page number 15.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate per annum is 9.0 %\n",
+ "sum is 1500.0 Rs\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",
+ "CI=282.15; #compound interest(Rs)\n",
+ "SI=270; #simple interest(Rs)\n",
+ "T=2; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "R=(CI-SI)*100*T/SI; #rate per annum(%)\n",
+ "P=100*SI/(R*T); #sum(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate per annum is\",R,\"%\"\n",
+ "print \"sum is\",P,\"Rs\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.9, Page number 15.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sum is 500.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=10; #rate(%)\n",
+ "T=3; #time(yrs)\n",
+ "CI_SI=31/2; #difference between CI and SI(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=R/100;\n",
+ "y=(x**3)+(T*(x**2));\n",
+ "P=CI_SI/y; #sum(Rs) \n",
+ "\n",
+ "#Result\n",
+ "print \"sum is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.10, Page number 15.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "ename": "ValueError",
+ "evalue": "math domain error",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-26-97e4181a1568>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 11\u001b[0m \u001b[0mDr\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m;\u001b[0m \u001b[1;31m#denominator of fraction\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[0md\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mNr\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mDr\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mNr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m \u001b[1;31m#discriminant\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m \u001b[0mq\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mNr\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0md\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mDr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m \u001b[1;31m#solution\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 15\u001b[0m \u001b[1;31m#Result\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mValueError\u001b[0m: math domain error"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=434;\n",
+ "b=272;\n",
+ "\n",
+ "#Calculation\n",
+ "Nr=a-b; #numerator of fraction\n",
+ "Dr=b; #denominator of fraction\n",
+ "d=(Nr**2)-(4*Dr*Nr); #discriminant\n",
+ "q=(-Nr-math.sqrt(d))/(2*Dr); #solution\n",
+ "\n",
+ "#Result\n",
+ "print \"value of q is\",q\n",
+ "print \"solution for the problem does not exist and the answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.11, Page number 15.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "annual payment is 18522.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "R=5; #rate(%)\n",
+ "A=50440; #debt amount(Rs)\n",
+ "T=3; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=100/(100+R);\n",
+ "y=x*(1+x+(x**2));\n",
+ "a=A/y; #annual payment(Rs)\n",
+ "\n",
+ "#Result\n",
+ "print \"annual payment is\",a,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.12, Page number 15.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time is 5.0 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=1; #assume\n",
+ "A=1.44*P; #amount(Rs)\n",
+ "T=2; #time(yrs)\n",
+ "N=2;\n",
+ "\n",
+ "#Calculation\n",
+ "R=(math.sqrt(A/P)-1)*100; #rate(%)\n",
+ "T=(N-1)*100/R; #time(yrs)\n",
+ "\n",
+ "#Result\n",
+ "print \"time is\",T,\"years\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.13, Page number 15.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate per annum is 6.0 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "I2=238.50; #interest in second year(Rs)\n",
+ "I1=225; #interest in first year(Rs)\n",
+ "T=1; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "I=I2-I1; #interest on 1 year(Rs)\n",
+ "R=100*I/(I1*T); #rate per annum(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate per annum is\",R,\"%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.14, Page number 15.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sum is 8000.0 Rs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "CI_SI=20; #difference for 2 years(Rs)\n",
+ "CISI=61; #difference for 3 yrs(Rs)\n",
+ "T1=2; #time(yrs)\n",
+ "T2=3; #time(yrs)\n",
+ "\n",
+ "#Calculation\n",
+ "R=((CISI/CI_SI)-T2)*100; #rate(%)\n",
+ "P=CI_SI*(100/R)**2; #sum(Rs) \n",
+ "\n",
+ "#Result\n",
+ "print \"sum is\",P,\"Rs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.15, Page number 15.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "rate per annum is 10.0 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=3; #time(yrs)\n",
+ "P=1000; #sum(Rs)\n",
+ "A=1331; #amount(Rs)\n",
+ "\n",
+ "#Calculation\n",
+ "x=(A/P)**(1/T);\n",
+ "R=100*(x-1); #rate per annum(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate per annum is\",R,\"%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 15.16, Page number 15.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time is 1.5 years\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "P=64000; #sum(Rs)\n",
+ "CI=4921; #compound interest(Rs)\n",
+ "R=5; #rate(%)\n",
+ "n=2;\n",
+ "\n",
+ "#Calculation\n",
+ "A=P+CI; #amount(Rs)\n",
+ "x=A/P;\n",
+ "y=(1+(R/(100*n)))**n;\n",
+ "T=math.log(x)/math.log(y); #time(years)\n",
+ "\n",
+ "#Result\n",
+ "print \"time is\",T,\"years\""
+ ]
+ }
+ ],
+ "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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