What will be the difference between simple and compound interest at the rate of 10% per annum on a sum of Rs. 1000 after 4 years?
Answer
Hint: To find the difference between the simple interest and compound interest, first calculate the simple interest and then compound interest then subtract simple interest in compound interest.
Complete step-by-step answer:
In the calculation of compound interest if we take small compounding time then the compound interest will be high as the compounding time will increase and the amount of compound interest will decrease.
Given the value of rate of interest =
10%
Principal = Rs 1000
Time = 4 years
We know that simple interest $ = \dfrac{{PRT}}{{100}}$
On putting the given values we get,
$\Rightarrow$ S.I. $ = \dfrac{{1000 \times 10 \times 4}}{{100}}$
S.I. $ = 400$ Rs
Similarly we will find the compound interest
$\Rightarrow$ We know compound interest = Amount−Principal
and amount is given by
$ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
On putting the given values we get
A = \[1000{\left( {1 + \dfrac{{10}}{{100}}}
\right)^4}\]
\[ = 1000 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \times
\Rightarrow \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}}\]
\[ = 1464.10\] Rs.
\[C.I. = 1464.10 - 1000 = 464.10\] Rs.
Now we will find the difference between C.I. and S.I.
Difference between C.I and S.I $464.10 - 400 = 64.10$ Rs.
Note: Compound interest is always higher than the simple interest for the same time period and same rate of interest only except the first year. In first year CI and SI are the same.
What will be the difference between simple and compound interest at the rate of 10% per annum on a sum of Rs. 1000 after 4 years?
A. Rs. 31
B. Rs. 32.10
C. Rs. 40.10
D. Rs. 64.10
Answer
Verified
Hint: We will first start by using the fact that simple interest on a principal P at a rate R for time T is $\dfrac{P\times R\times T}{100}$ whereas the compound interest on a principal P at a rate R for time T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Then we will find its difference to find the answer.Complete step-by-step solution -
Now, we have been given a principal amount of Rs. 1000, the interest is 10% per annum for a period of 4 years.
Now, we know that the
simple interest on a principal P at a rate of R for T years is $\dfrac{P\times R\times T}{100}$. So, using this we have simple interest $=\dfrac{1000\times 4\times 10}{100}=Rs.400$.
Now, we know that compound interest on a principal P at a rate R for a period of T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$.
$\begin{align}
& =1000{{\left( 1+\dfrac{10}{100} \right)}^{4}}-1000 \\
& =1000{{\left( 1+\dfrac{1}{10} \right)}^{4}}-1000 \\
& =464.1
\\
\end{align}$
Hence, the difference between compound interest and simple interest is,
$\begin{align}
& 464.1-400 \\
& =64.1 \\
\end{align}$
Hence, the correct option is (D).
Note: It is important to note that we have used a fact that for finding SI on a principal amount P at a rate R for a period of T is $\dfrac{P\times R\times T}{100}$ and for compound interest for the same, conditions is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Also, it is important to remember that compound interest is always greater than simple interest.
Mohammed
Guys, does anyone know the answer?
get what is the difference between simple and compound interest on rupees 1000 at 10% for 5 years from screen.
Click here👆to get an answer to your question ✍️ What will be the difference between simple and compound interest at 10
Question
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
A
Rs. 31
B
Rs. 32.10
C
Rs. 40.40
D
Rs. 64.10
Easy Open in App Solution Verified by Toppr
Correct option is D)
Principal=1000 Rs.
Time=4 years Rate of interes=10%
Then Simple interest =
100 1000×10×4 =400Rs.
Compound interest = Amount − Principal
Amount =1000(1+ 100 10 ) 4 ⇒1000× 100 110 × 100 110 × 100 110 × 100 110 × ⇒1464.10Rs.
C.I.=1464.10−4000=464.10Rs.
Difference between C.I and S.I.=464.10−400=64.10Rs.
Was this answer helpful?
34 5
स्रोत : www.toppr.com
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years? - Get the answer to this question and access other important questions, only at BYJU’S.
Academic QuestionsMaths QuestionsWhat Will Be The Difference Between Simple And Compound Interest At 10 Per Annum On A Sum Of Rs 1000 After 4 Years
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
Principal = 1000 Rs.
Time = 4 years
Rate of interest = 10%
Was this answer helpful?
4 (3)
Related Questions & Answers
Can Real Image Be Obtained On The Screen
Which Element Have Highest Ionisation Potential
How Can One Classify Ethers
Give An Example Of Combination Reaction Between Two Elements
Can Paints Have Dispersed Particles
Lion Cat And Tiger Belong To A Common Fill In The Blank
Ac And Dc Both Can Be Measured By
Name The Regions In Which Parenchyma Tissue Is Present
What Are The Different Types Of Water Energy
The Magnification Of A Convex Mirror Is Always
स्रोत : byjus.com
What will be the difference between the simple and compound interest on Rs. 1000 at the rate of 10% per annum in 4 years? Please explain the answer in brief
Find 9 Answers & Solutions for the question What will be the difference between the simple and compound interest on Rs. 1000 at the rate of 10% per annum in 4 years? Please explain the answer in brief
Mathematics Question:
What will be the difference between the simple and compound interest on Rs. 1000 at the rate of 10% per annum in 4 years? Please explain the answer in brief
A Rs. 62.10 B Rs. 63.10 C Rs. 64.10 D Rs. 65.10 E Rs. 66.10
Posted by: Ketikamanohar on 05.10.2017
Ask a Question
9 Answers by Expert Tutors
Like Add to Favorite Follow Share
Get Answers in Email
Answered by: V
Vijay G. from Mumbai
Like Answer: Ans. C
Diff, between CI and SI = Dif. between the Amounts = Rs.1000[(1 + 10/100)^4 - (1 + 10*4/100)] = Rs.1000[1.4641 - 1.4] = Rs. 64.10 .
Answered by: S Sumi from Hyderabad Like Answer:
The Diff, between CI and SI = Dif. between the Amounts
so Rs.1000[(1 + 10/100)^4 - (1 + 10*4/100)]
= Rs.1000[1.4641 - 1.4]
= Rs. 64.10 . Answered by: K
Kshitij G. from Noida
Like Answer:
Simple interest=P*R*T/100, SI=(1000*10*4)/100=400, CI=A-P, A=P(1+r)^n,A=1000(1.1)^4A=1464.1,CI=464.1,Difference between CI and SI=64.1(option C)
Answered by: K
Kavitha from Chennai
Like Answer:
Compound interest=P(1+4/100)^4-1) =1000(104/100)^4-1) =1000(14641-10000/10000) Compound interest =464.1 Simple interest=PNR =1000*10/100*4=400 Difference between compound interest and simple interest=464.1-400=64.10 Correct answer is C
Answered by: V
Vinita K. from Siliguri
Like Answer: Option C = 64.10
Simple Interest for four years = Principle * rate of Interest * No. of years
=> 1000* 10/100 * 4 => Rs. 400
Compound Interest
1st Year Interest = Principle * rate of Interest
=> 1000*10/100 = Rs. 100
2nd Year Principle = Principal + Interest => 1000+100 = Rs. 1100
2nd Year Interest = 1100*10/100 => Rs. 110
3rd Year principal = 1100+110 = Rs. 1210
3rd Year Interest = 1210*10/100 => Rs.121
4th Year principal = 1210+121 = Rs. 1331
4th Year Interest = 1331*10/100 => Rs 133.10
Total 4 years Compound interest => 100+110+121+133.10 = Rs. 464.10
Difference = Compound Interest - Simple Interest
=> 464.10 - 400 = Rs. 64.10
Answered by:
S.Chandra from Kolkata
Like Answer:
Ans. Option C (Rs. 64.10)
Diff, between CI and SI = Dif. between the Amounts = Rs.1000[(1 + 10/100)^4 - (1 + 10*4/100)] = Rs.1000[1.4641 - 1.4] = Rs. 64.10 .
Answered by:
Shubham B. from Kolkata
Like Answer:
Principal sum = ₹1000, interest rate = 10%p.a. , time= 4yrs. Simple interest= P.R.T/100 = 1000×10×4/100 = 400. Compound interest= P{1+ R/100}™ - P =1000{1+10/1000}^4-1000 = 1464.1 - 1000 = 464.1 Thus difference in interests= 464.1 - 400 = ₹64.1. Option C.
Answered by:
Kamakshi B. from Delhi
Like Answer: Option C
Answered by: A Ankit from Delhi Like Answer:
Simple interest => Amount= principal(1+rate*time/100) I.e, 1000(1+10*4/100) We get;1400 Compund interest=> Amount=p[1+r/100]^n I.e, 1000[1+10/100]^4 We get; 1000[1.1]^4 1000[1.4641] 1464.1 Difference between both interest is 1464.1-1400=64.1 So, Option c is the correct answer
Post Answer and Earn Credit Points
Get 5 credit points for each correct answer. The best one gets 25 in all.
Post Answer Similar Questions
Posted by: Parneet S.
Answer all this please
Posted by: samantha
Solve the substitution method, elimination method, cross multiplicatio...
Posted by: harjot
Plz Give the solution
Posted by: Ommkar S.
Plz Give the solution
Posted by: Ommkar S.
Plz Give the solution
Posted by: Ommkar S.
Plz Give the solution
Posted by: Ommkar S.
Solve by substitution method, elimination method and cross multiplicat...
Posted by: harjot
If one zero of the quadratic polynomial 2x^2 - 6kx +6x -7 is negative ...
Posted by:
If -4 is a zero Of the polynomial x^2 - x - (2k+2) then k=
Posted by: Sradha Topic Cloud
.Net 2D Animation 3D Animation 3D Max / Maya 3D Printing Abacus Teachers Training Abacus Training ACCA ACCA Training Accent Training Accessory Making Accountancy Accounts ACET Acrobatic Acrylic Painting ACS ACT Exam Acting & Drama Actuarial Science Administrative Laws Adobe After Effects Certification Adobe Certification Adobe Premiere Pro Certification Adobe Tools Advanced Excel Advanced Maths Adventure Camps Aero Modelling Aeronautical AFCAT African Painting Agriculture AICEE AIEED AIEEE AIIMS AIPG Exam AIPMT Aircraft Engineering AJAX Training Algebra All Subjects AMAESI AMIE AMITE Anatomy Andhra Folk Android Training Angular JS Animal Yoga Animation Animation Drawing Ansys Workbench Anthropology App Store Optimization Apparel Designing Appium Certification Apps Development APSET Exam Architecture Arduino Programming Artificial Intelligence (AI) Assamese Astrology Auditing AutoCAD Training Autodesk Maya Automobile Engineering B.A. Tourism B.Arch Tuition B.Com Tuition B.Ed Tuition B.Sc Tuition B.Tech Tuition BA Tuition Baal Geet Bachelor of Hospital Administration (BHA) Bachelor of Tourism Administration Bag Making Ballet Ballroom Dance Bank Clerical Bank PO Banking & Finance Basic Computer Batik Art BBA BBA Entrance BBA Subjects BBA Tuition BBE Exam BBM BCA BCA Entrance BCA Subjects BCA Tuition BDS Bead Craft Behavioral Science Belly Bengali BFIA Exam Bhajan Bhakti Songs Bharat Natyam Big Data & Hadoop Bio Chemistry Bio Technology Bio-informatics Bio-medical Biology BITSAT Block Painting Blockchain Blog Programming BMS Tuition Bolly Hop Bolly Jazz Bollywood Bollywood Fusion Bootstrap Botany Bouquet Making Brainobrain Bread Craft Break Dance Brownies Business Analytics Business Economics Business English Business Etiquette Business Law Business Management Business Mathematics Business Organisation Business Statistics Business Studies Business System & Infrastructure Management C, C++ C# (C Sharp) CA - CPT CA - Final CA Foundation CA Intermediate Cake Decoration Cake Making Calligraphy Candle Making Canvas Painting Card Making Carnatic Dance Carnatic Vocal Cartooning CAT Exam CCNA Certification CCNA Cyber Ops CDS/OTA Exam CEED Ceramic Painting Certificate in Stock Markets CET CFA Cha Cha Charcoal Painting Chemical Chemistry Chhau Chinese Chocolate Making Chocolate Puddings Choreography Classes Cisco certification Civics Civil Civil Laws Classical Vocal Classical Western Vocal CLAT Clay Craft Clay Modelling Clay Molding Clay Painting Cloud Computing CMA Intermediate CMA-CPA-ACCA-CIMA CMAT CMSE Exam Coding & Programming Coldfusion Collage Combo Organ COMEDK Exam Commerce Subjects Communicative English Computer Computer for official job Computer Hardware Computer Science Constitutional Law Contemporary Content Marketing Content Writing Continental Cooking & Baking Cooperative Accounting Corel Draw Corporate Accounting Corporate Communication Corporate Finance Corporate Laws Costing Crayons Painting Creative Writing Classes CSAT CSEET Exam CSS Training CTET CUET Exam Cultural Music Cupcake Cutting & Pasting CWE Coaching Cyber Security Certification Dandiya Data Analysis Certification Data Entry Data Mining Data Science Data Structures DBMS & RDBMS Debate Decoration Decoupage Defence Exams Dell Boomi Certification Demandware Training Courses Desserts DevOps Certification Devotional Dance Devotional Songs Dhangar Dance Digital Marketing Diya Decoration Diya Making Drawing & Painting Dreamweaver Drupal Dry Painting DSC Exam DTP DU JAT Exam E-Commerce e-Filing EAMCET Economics Education Effective Communication Egyptian Painting Electrical Electronics Electronics and Communication Embedded Systems Emboss Painting Engineering Design Engineering Graphics English Enterprenuership Envelope Making ERP Training ESI Exam Ethical Hacking Event Management EVS Fabric Craft Fabric Painting Facebook Applications Fashion Designing Fashion Study FDDI Film Making Finance Financial Management Financial Reporting Fine Art Fitness Centre Flash Floor Exercise Flower Making Folk Art Food & Nutrition Food Inspector Exam Forest Department Exam Forex Trading Frame Making French Freshbooks Fusion Garba GAT Exam GATE Exam Gaudiya Nritya General Knowledge Geography Ghazal GIC Glass Craft Glass Painting Glitter Painting GMAT GOAT Gondhal GPAT Graphic Designing GRE GSEB GUJCET GST Certification Training GST Training Gujrati Folk Gurmat Sangeet HACCP Hand Painting Handicrafts Hardware Training Hariyanvi Folk Harmonium Hindi Hindustani Classical Vocal Hindustani Vocal Hip Hop HIPAA Training History Home Science Hotel Management Hotel Management Entrance HR/Personnel HTML Training Human Anatomy Human Resource Human Resource and Marketing IAS Preparation IBM Training IBPS IBPS PO Ice Cream Making ICT Training ICWA & ICWAI IELTS IIM Exam IIMC Entrance Exam IISER Exam IIT JAM IIT JEE Advanced IIT JEE Mains Illustrator Import & Export Income Tax Indian Classical Dance Indian Classical Vocal Indian Contemporary Indian Folk Indian Modern Dance Indian National Mathematical Olympiad (INMO) Indirect Tax Informatica Information Practice Informix Training Inorganic Chemistry Instrumentation Insurance Exams Interior Designing International Business Marketing iOS Training IoT Certifications IPMAT IPS Exam ISI Exam IT & Commerce IT & Computer Subjects Italian Japanese Java and J2EE Java Script Jazz JECA Exam JELET Jewellery Design JIPMER Joomla Training Journalism/Writing jQuery Judicial Services Jungle Art Jute Craft Karnataka Folk KARTET Exam KAS Exam Kathakali Kids Gym Kolattam Dance KPSC Exam Kuchipudi Lamasa Art Laravel Law Entrance LDC Exam Lego Programming LIC Light Classical Vocal Light Vocal LLB LNAT Exam Logic M Seal Craft M.Tech Tuition MA Tuition Machine Learning Madhubani Painting Magento Training Magic Malayalam Management Subjects Manipuri Manual Testing Marathi Folk Marble Painting Marketing Training Martial Arts Mask Making Mass communication Mathematics MATLAB MBA MBA Entrance MBBS Tuition MCA MCA Entrance MCA Entrance Exam (JECA) MCA Subjects MCAT MDS Exam Mechanical Mechanics Medical Transcription Mehendi Mental Mathematics Mexican Mexican Painting MicroBiology Microsoft Azure Certification Microsoft Certification Minakari Art Miniature Painting MIS Training Mocktail Mocktail Making Mohiniyattam Molding Craft MongoDB MS Office MSBI Certification Mughlai MuleSoft Certification Municipal Service Commission Exams Mural Painting Mysore Painting Nail Painting NATA Exam Nattuvangam NBDE NDA NDEB Exam NEET NEST NET Networking Nib Painting NID NIMCET NIOS Nip Painting NIRRH NISM NMIMS Exam NMSQT No Flame Cooking Node JS North Indian NPAT Exam NPTT NTT Oil Painting Olympiad Exam Preparation Oracle Certification Oracle RDBMS Oracle Training Oratory Organic Chemistry Origami Page Maker Paper Craft Parchment Craft Pastel Painting PCS Exam Pega Certification Pencil Drawing Perl Programming Personality Development PET Exam PG Diploma PG Medical Pharmacy Philosophy Photography Photoshop PHP and MySQL Physical Development Physics Physiology Pilates PL/SQL PLAB 1 Exam Preparation PLAB 2 Exam Preparation Play Gym Political Science Polytechnic Pop Classes Portrait Poster Colour Painting Poster Making Pot Painting Pottery Power BI Certification Power Yoga Production Programming Language Project Management PSAT PSC Exam PSU Exam Psychology PTE PTT Public Administration Public Speaking Puddings Punch Craft Punjabi Puppet Making Purse Making Python Programming Quickbooks Quilling Rabindra Sangeet Railways Exams Rajasthani Folk Rajasthani Painting Rangoli Raspberry pi Programming RBI Exam React JS React Native Training Reading Skills Recitation Regional Mathematical Olympiad (RMO) Remo 3D Retail Management RHCE Training Rhyme & Chime Rhythmic Rhymes Robotics Rock n Roll RRB RRB JE RRB NTPC Exam SaaS Salad Making Sales Training Salesforce Certification Salesforce CRM Sand Art Sandwich Making Sanskrit Santoor SAP Training SAS Certifications SAT Sattriya SBI Exam School level computer School Level Training Science Scrapbooking Sculpture Making SEBI Exam Selenium Training Semi Classical Dance Semi Classical Vocal Sewing Shell Scripting Shetkari Shipping & Logistics Shlokas Simulation Design Singing Six Sigma Certification Training SLET Exam Social Studies Sociology Soft Skills Software Engineering Software Testing SOP Writing South Indian Special Effects Speech & Drama Spoken English Squash SSB Exam SSC CGL Exams SSC Exams SSC JE Statistics Stenography and Shorthand Stock & Share Trading Story Telling Strategic Business Reporting Sub-Inspector Exam Sufi Sugam Sangeet Sugar CRM Sun Certification Swimming Synthesizer Tailoring & Knitting Tally ERP 9 Tango Tanjore Painting Tap Tattoo Painting Tax Laws Taxation Telegraph Painting Textile Designing Theme Cooking Tibco Certification Tie & Dye Tile Painting TISS BAT Exam TISSMAT Exam TOEFL TOEIC TOPIK Exam Toy Making Traditional UGC Exams UGC Net UKCAT Unix/Linux UPESEAT Exam UPPSC Exam UPSC Exam Urdu Vedic Maths Vegetarian Video Editing Visual Basic Vmware Waltz Warli Painting Water Colours WBCS WBJEE Web Designing Web Development Weblogic WebMethod Developer WebMethods Certification Websphere Western Vocal Wheel Pottery Woodwork Wordpress Training Writing Skills XAT Yoga Zend Framework Zoho CRM Zoology Zumba
स्रोत : www.learnpick.in