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• RD Sharma Class 8 Maths Solutions Chapter 14 - Compound Interest
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RD Sharma Solutions for Class 8 Maths - Compound Interest - Free PDF Download

Compound interest is the addition of interest, or, in other words, interest on interest, to the principal amount of a loan or deposit. Instead of paying it back, it is the product of reinvesting interest, so the interest is then paid on the principal sum plus already accrued interest in the next cycle. Compound interest deals with the money-related issue so it is important for Class 8 students to understand the concepts clearly. RD Sharma Class 8 Maths Solutions Chapter 14 provides exclusive content about Compound interest and solutions to important questions.

RD Sharma Solutions For Class 8 Maths Chapter Compound Interest is based on the NCERT curriculum and CBSE syllabus. These solutions will help students to prepare for their board exams as well as apply these concepts in their real-life situations too. Students can download Compound Interest Class 8 RD Sharma Solutions free PDF available on the Vedantu platform. Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful. Download Class 8 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Class 8 RD Sharma Textbook Solutions Chapter 14 - Compound Interest

You can download RD Sharma Class 8 Maths solutions for Chapter 14 Compound Interest from the website of Vedantu.

Vedantu has provided step-by-step solutions for all exercise questions given in the pdf of Class 8 RD Sharma Chapter 14 - Compound Interest. All the Exercise questions with solutions in Chapter 14 - Compound Interest are given below:

Exercise 14.1

Exercise 14.2

Exercise 14.3

Exercise 14.4

Exercise 14.5

The Compound Interest Class 8 RD Sharma Solutions are developed by experts who have a lot of experience in teaching the subject. These solutions are carefully designed in a step-by-step manner with the utmost care to make students understand the concepts easily and ace their exams.

Here, let us look into a few of the important topics from the Compound Interest chapter which are frequently asked in the exams.

Computation of compound interest annually.

Computation of compound interest half-yearly.

Computation of compound interest quarterly.

Computation of compound interest by using Formulae.

Inverse problems on compound interest.

Population growth problems.

Depreciation related problems.

Exams Preparation Tips using RD Sharma Solutions for Class 8 Maths Chapter Compound Interest

These tips will come in handy for students while attempting any questions from the Compound interest chapter.

Recall the concepts of ratios and percentages before attempting the questions from Compound interest.

Understand the concepts of simple interest, profit and loss and discounts clearly and then start with the compound interest concept.

Remember the basic formulas of simple interest and compound interest to solve the questions in quick time.

The Compound Interest Class 8 RD Sharma Solutions prepared by Vedantu experts will be really helpful for students when preparing for their board exams. The RD Sharma solutions also have a lot of practice questions for students to prepare for their exams with more confidence. The solutions are designed in such a way that students will get a unique and fun way of learning when referring to the RD Sharma Class 8 solutions on Compound interest.

FAQs on RD Sharma Class 8 Maths Solutions Chapter 14 - Compound Interest

1. What is Compound Interest?

Compound interest refers to the process in which the interest associated with a savings account, loan, or investment rises over time exponentially instead of linearly. It is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest.

2. Why does one have to study RD Sharma solutions for Class 8 Maths chapter Compound Interest?

RD Sharma is a highly recommended book by toppers and experts to score better in the exam. Students are advised to practice all the questions given in the exercise for a better understanding. They can refer to previous year questions and other free PDFs available on Vedantu for comprehensive knowledge. Vedantu also has free material by RD Sharma and carefully made solutions to all of it. Students can access it from the website and its mobile application. They can also download it from the links below and study offline.

3. What is the formula to calculate compound interest?

The formula to calculate compound interest is CI = P[(1 + R)^nt – 1].

CI denotes compound interest

P = principal amount

R = rate of interest

n = number of compounding years

t = time (in years)

Compound interest is an interest paid on a loan or certain amount of money. It depends on both the principal and interest accumulated over a certain time. This is what differentiates it from simple interest. If the interest differs every year and gets increased if we stop paying every month then we can say the loan is charged with compound interest. It is used to calculate changes in population and computing growth of bacteria etc.,

4. What is the formula to calculate compound interest on a daily basis?

The formula to calculate compound interest is:

A = P(1 + r/365)^{365 * t}

P = principal

t = time period

Compound interest is an interest charged on a certain sum of money. It can be calculated annually, quarterly and half - yearly. Compound interest is charged on the principal amount and the interest. This is the difference between simple and compound interest. Simple interest is calculated just on the principal amount. Generally banks offer loans for compound interest. If you look at the bank statement  and find the interest rate changing every year and increasing then you can understand that you are being charged with compound interest.

You can avail all the well-researched and good quality chapters, sample papers, syllabus on various topics from the website of Vedantu and its mobile application available on the play store. 

5. What is the Difference Between Simple Interest and Compound Interest?

Simple interest is based on a principal or initial amount. Compound interest shall be measured on the principal sum as well as on the accrued interest of the intervening periods and can therefore be known as interest on interest.

RD Sharma Class 8 Maths Solutions

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Class viii math, class-8 compound interest, introduction to compound interest, deducing a formula for compound interest, conversion period, compound interest for different interest rate, compound interest when the total time is not a complete number of conversion periods.

Compound Interest Worksheet

Answer Sheet

Bank, post office, insurance companies calculate the interest for one year and then yearly interest is added to the principal. The amount we get becomes the principal for second year interest calculation. This process is repeated until the amount is calculated for the whole loan period.

Thus, the difference between the final amount and the original principal is called the compound interest. It is written as C.I. C.I = A − P

Note: The principal remains constant for the whole loan period in case of simple interest calculation, but the principal keeps on changing every year for compound interest calculation.

Example 1. Calculate the compound interest on 20,000 rupees for 2years at 4% per annum. Solution. Here, rate of interest = 4%, principal for the first year = Rs. 20,000. Interest for the first year = 20,000 × 4 × 1 ⁄ 100           = Rs. 800 Amount at the end of first year = 20,000 + 800 = Rs. 20,800. Principal for the second year = Rs. 20,800 Interest for the second = 20,800 × 4 × 1 ⁄ 100 = Rs. 832 Amount at the end of second year = 20,800 + 832 = Rs. 21,632 Compound interest for 2 years = final amount − original           = 21,632 − 20,000 = Rs. 1632.

Example 2. Mohan invests 15000 rupees for 3 years at 5% per annum compound interest in bank. Find out the compound interest for the second year and for the 3rd year. Solution. Here, rate of interest = 5% Principal for the first year = Rs. 15,000. Interest for the first year = 15,000 × 5 × 1 ⁄ 100           = Rs. 750 Amount at the end of first year = 15,000 + 750           = Rs. 15,750 Principal for the second year = Rs. 15,750 Interest for the second = 15,750 × 5 × 1 ⁄ 100           = Rs. 787.50 Compound interest for the second year = Rs. 787.50 Amount at the end of second year = 15,750 + 787.50           = Rs. 16,537.50 Principal for the third year = Rs. 16,537.50 Interest for the third year = 16,537.50 × 5 × 1 ⁄ 100           = Rs. 826. 87 Compound interest for the third year = Rs. 826.87.

Example 3. Calculate the simple interest and compound interest on 20,000 rupees for 2 years at 5% per annum. Solution. For simple interest, Principal for the first year = Rs. 20,000 Rate of interest = 5% per annum Interest for first year = 20,000 × 5 × 1 ⁄ 100           = Rs. 1000 Amount at the end of first year = 20,000 + 1000           = Rs. 21,000 Principal for the second year = Rs. 21,000 Interest for the second = 20,000 × 5 × 1 ⁄ 100           = Rs. 1000 Amount end of second year = 21,000 + 1000           = Rs. 22000 Interest earned by simple interest in 2 years = Rs. 22000 − Rs. 20,000           = Rs. 2000 For, compound interest principal for the first year = Rs. 20,000 Rate of interest = 5% per annum Interest for first year = 20,000 × 5 × 1 ⁄ 100           = Rs. 1000 Amount at the end of first year = 20,000 + 1000           = Rs. 21,000 Principal for the second year = Rs. 21,000 Interest for the second = 21,000 × 5 × 1 ⁄ 100           = Rs. 1050 Amount end of second year = 21,000 + 1050           = Rs. 22050 Interest earned by compound interest in 2 years = 22050 − 20,000           = Rs. 2050 Now according to question, difference of S.I and C.I is = 2050 − 2000           = Rs. 50

To find out compound interest in shorter way, following formulae we should use. Let's discuss how formulae formed.

Suppose a sum of P rupees is compounded annually at a rate of R % per annum for n year. The amount at the end of n years must be calculated by using formulae            A = P(1 + R ⁄ 100 ) n            Compound Interest (C.I) = A − P

Let's see some solved examples for better understanding

Example 1. What principal of money will amount to Rs. 2205 in two years at 7% per annum compound interest? Solution. Here, A = Rs. 2205, R= 5%, n = 2 years A = P(1 + R ⁄ 100 ) n ⇒ 2205 = P(1 + 5 ⁄ 100 ) 2 ⇒ 2205 = P( 21 ⁄ 20 ) × ( 21 ⁄ 20 ) ⇒ P = 2205( 21 ⁄ 20 ) × ( 21 ⁄ 20 )           = Rs. 2000 Hence the principal is Rs. 2000.

Example 2. Find compound interest on 15,500 rupees for 2 years at 10% per annum. Solution. Given P = Rs. 15,500, T = 2 years, R = 10% Here, we first find out Amount (A) = 15,500 (1 + 10 ⁄ 100 ) 2           = 15,500 (1 + 1 ⁄ 10 ) 2           = 15,500 × 11 ⁄ 10 × 11 ⁄ 10           = Rs. 18,755 C.I = A − P = 18,755 − 15,500 = Rs. 3,255 Hence, the compound interest is Rs. 3,255.

The interest is added every time after a specified period to form a new principal amount. This period is known as conversion period. If interest is compounded annually, then one conversion period is considered in one year. If interest is compounded semi-annually, then two conversion period is considered in one year. Similarly, if interest is compounded quarterly, then four conversion periods is considered in a year.

Example 1. Calculate the amount should be paid at the end of 3 months on Rs. 2800 at 5% per annum compounded quarterly. Solution. As rate of interest is 5% per annum Then, rate of interest quarterly is = 5 ⁄ 4 % As the amount to be paid in 6 month, so, n = 4 quarters According to question, A = P(1 + R ⁄ 100 ) n           = 2800{1 + ( ( 5 ⁄ 4 ) ⁄ 100 )} 4           = 2800 (1 + 5 ⁄ 400 ) 4           = 2800(1 + 1 ⁄ 80 ) 4           = 2800 × ( 81 ⁄ 80 ) × ( 81 ⁄ 80 ) × ( 81 ⁄ 80 ) × ( 81 ⁄ 80 )           = Rs. 2942.64 Hence, 2942.64 rupees to be paid at the end of 3 months.

When the rates of interest for the successive conversion periods are R 1 %, R 2 %, R 3 %, ...and principal is P . Then, amount A is calculated by using the formulae. A = P(1 + R 1 ⁄ 100 ) × (1 + R 2 ⁄ 100 ) × (1 + R 3 ⁄ 100 ) × ... so on And the calculate compound interest (C.I) = A − P.

Example 1. How much will Rs. 20,000 amount in 2 years at compound interest, if the rates for the successive years are 5% and 6% per year? Solution. P = Rs. 20,000, R 1 = 5% and R 2 = 6% A = P(1 + R 1 ⁄ 100 ) × (1 + R 2 ⁄ 100 )           = 20,000(1 + 5 ⁄ 100 ) × (1 + 6 ⁄ 100 )           = Rs. 1,11300

If total time period is not a complete number of conversion period, then we should calculate the amount as simple interest for partial time period.

Consider time is given 2 years 4 months and interest is R% per annum compounded annually, then amount A is calculated by using formulae. A = P(1 + R ⁄ 100 ) 2 × [1 + ( 4 ⁄ 12 ) × R ⁄ 100 ] Then find out compound interest using C.I = A − P

Example 1. Calculate the amount and compound interest on Rs. 25,000 compounded annually for 3 1 ⁄ 2 years at 2% per annum. Solution. Here P = Rs. 25000, R = 2%, T = 3 1 ⁄ 2 years A = 25000(1 + 2 ⁄ 100 ) 3 × {1 + ( 6 ⁄ 12 ) × 2 ⁄ 100 }           = 25000 × ( 51 ⁄ 100 ) 3 × {1 + ( 1 ⁄ 100 )}           = 25000 × ( 51 ⁄ 100 ) × ( 51 ⁄ 100 ) × ( 51 ⁄ 100 ) × ( 101 ⁄ 100 )           = Rs. 26795.50 Then calculating Compound interest C.I = A − P C.I = 26795.50 − 25000 = Rs. 1795.50

Class-8 Compound Interest Worksheet

Compound Interest Worksheet - 1

Compound Interest Worksheet - 2

Compound-Interest-Answer Download the pdf

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Video transcript

ICSE / ISC / CBSE Mathematics Portal for K12 Students

Mathematics made easy for school students.

Class 8 , Lecture Notes - Simple Interest & Compound Interest , Simple Interest and Compound Interest

Class 8: Simple Interest and Compound Interest -Lecture Notes

Introduction to various terms used in Simple Interest and Compound Interest:

Principal: This is the money borrowed or lent out for a certain period of time is called the principal or sum.

Interest: Interest is payment from a borrower to a lender of an amount above repayment of the principal sum

Amount: The total money paid back by the borrower to the lender is called the amount.

Rate: The interest on Rs. 100 for a unit time is called the rate of interest. It is expressed in %. The interest on Rs. 100 for 1 year is called rate % per annum (abbreviated as rate % p. a.)

Simple Interest

• Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains. It excludes the effect of  compounding . It is denoted by S.I.
• The simple interest is calculated uniformly only on the original principal throughout the loan period.
• You do not earn interest on the interest earned during the loan period.

• While calculating the time period between two given dates, the day on which the money is borrowed is not counted for interest calculations while the day on which the money is returned, is counted for interest calculations.
• For converting the time in days into years, we always divide by 365, whether it is an ordinary year or a leap year.

Compound Interest

• Compound interest includes interest earned on the interest which was previously accumulated.
• Here you also earn interest over the interest accrued during the loan period.
• The difference between the final amount and the original principal is called the compound interest (abbreviated as C.I.)

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Chapter 1: Rational Numbers

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• Representation of Rational Numbers on the Number Line | Class 8 Maths
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Chapter 2: Linear Equations in One Variable

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Chapter 4: Practical Geometry

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Chapter 5: Data Handling

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• Sales Tax, Value Added Tax, and Goods and Services Tax - Comparing Quantities | Class 8 Maths
• Simple Interest

Compound Interest | Class 8 Maths

• Compound Interest Formula

Chapter 9: Algebraic Expressions and Identities

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Chapter 10: Visualising Solid Shapes

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Compound Interest: Compounding is a process of re-investing the earnings in your principal to get an exponential return as the next growth is on a bigger principal, following this process of adding earnings to the principal. In this passage of time, the principal will grow exponentially and produce unusual returns.

Sometimes we come across some statements like “one year interest for FD in the bank @ 11 % per annum.” or “Savings account with interest @ 8% per annum”.  When it comes to investment, there are usually two types of interests :

Compound Interest

We already know about Simple Interest(S.I), we will look at Compound Interest(C.I) in detail in this article. First, let’s understand what is compounding through a story. 

A Prisoner was once awaiting his death sentence when the king asked for his last wish. The Prisoner demanded grain of rice (foolish demand right?) but added that the number of grain should be doubled after moving to every square till the last square of the Chess Board ( that is 1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square). The king thought that it is a very small demand and ordered his ministers to have that much amount of rice calculated and provided to the prisoner. The amount calculated was so big that the king lost his entire kingdom and was indebted to prisoner all of his life.

What the prisoner used was the idea of “ Compounding “. Now, let’s define Compound Interest. 

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. Let’s see an example before working out the formula, 

Question: Hema borrowed a sum of Rs. 2,00,000 for 2 years at an interest of 8% compounded annually from a bank. Find the Compound Interest and the amount she had to pay at the end of 2 years.

Answer : 

To do it, we need to find interest year by year. Step 1. First let’s find Simple Interest for the first year,           Here, principal P 1 = 2,00,000, R = 8% and T = 1.           SI 1 = SI at 8% on P 1 for one year =  Step 2. So, now the amount received at the end of the first year = SI 1 + P 1 = 16000 + 2,00,000 = 2,16,000. Now, this will become principal.             Thus, P 2 = 2,16,000, R = 8 and T = 1 Step 3. Now we will find simple interest for the second year by taking the total amount at the end of 1st year as principal P 2 .            SI 2 = SI at 8% on P 2 for one year =            This amount now at the end of 2nd year = SI 2 + P 2 = 17280 + 2,16,000 = 2,33,280            Total interest given = 17280 + 16000 = 33280., We need to notice that Principal remains the same in Simple Interest(SI), but in Compound Interest(CI) it recalculated and changes every year. 

Formula for Compound Interest

Let’s derive the formula for compound interest by taking the previous example only, but this time we will not use the values for the variables.     Now, the amount at the end of first year will the principal for the second year, i.e So, now SI for 2nd year Calculating the amount for the 2nd year, Now using the value of P2 in the above equation, Similar if we keep calculating for “n” years, We’ll end up with this formula of amount where P is the initial principal amount, R is the rate and n is the number of years after which the amount is calculated. 

Rate Compounded Annually or Half Yearly

You may notice that, in the beginning, we used “rate compounded yearly”. What does it mean?

It means that interest was compounded once a year. We can also have our interest compounded half-yearly or quarterly. What happens in such cases?

Let’s compare the two cases through an example to see the difference between rates compounded yearly and half-yearly. 

Suppose P = 1000, R = 5% and n = 2 years, Case 1: Interest compound annually. A = 50 + 1000 = 1050. Case 2: Interest Compounded Half-Yearly. P 2 = I + P = 1025 Final amount in this case A = P 2 + I 2 = 1025 + 25.625 = 1050.625  

We can that if interest is compounded half-yearly, compute the interest two times. So the time period becomes twice and the rate is taken half.

So the formula becomes, 

Applications of Compound Interest

Below are some of the applications of compound interest in real life:

Growth and Decay

The compound interest concept can be applied to any quantity which increases or decreases such that the amount at the end of each period bears a constant ratio to the amount at the beginning of that period.

Question: The population of a town increases at the rate of 2.5% annually. If its present population is 3,26,40,000, find the population after 3 years.

We can apply compound interest formula here, Population “P” at the end of 3 years will be,

Appreciation and Depreciation

When the value of an article increases with the passage of time, the article is said to appreciate. When the value of an article decreases with the passage of time, the article is said to depreciate.

For example, if a man buys a car and uses it for two years, it is obvious that the car will not be worth it as a new one. The car will thus have depreciated in value. On the other hand, if a man buys a piece of land, he will probably find that in a few years he will be able to get a better price for it than the price he paid for it. The value of the land will thus have appreciated. When things are difficult to obtain, they have a rarity value and appreciation.

Question: The value of a residential flat constructed at a cost of Rs 10,00,000 is appreciating at the rate of 10% per year annum. What will be its value 3 years after construction?

Value of flat P = 1000000, rate of appreciation = 10, n = 3 After 3 years, let the value of flat be “A”. So, after 3 years value of flat will be 13,31,000. 

The growth of a bacteria if the rate of growth is known:

Question: In a certain experiment, the count of bacteria was increasing at the rate of 2.5% per hour. Initially, the count was 51,20,000. Find the bacteria at the end of 2 hours.

Answer:  

Initial count of bacteria = P = 51,20,000, Increase rate “r” = 2.5 per hour, We want to find the count after 2 hours, i.e; n = 2 Let the final count be “A” So, the final count of bacteria is 53,79,200. 

Compound Interest Class 8 Questions

1. A sum of $5000 is invested at an annual interest rate of 8% compounded annually. Find the amount of money after 3 years.

2. If the principal amount is $2000 and the annual interest rate is 10%, calculate the compound interest for 2 years when interest is compounded annually.

3. Find the compound interest on $3000 for 2 years if the rate of interest is 5% per annum compounded annually.

4. A sum of $8000 is invested at a compound interest rate of 6% per annum. Calculate the amount after 2 years.

5. If the compound interest on a certain sum of money for 2 years at 10% per annum is $630, find the principal amount.

FAQs on Compound Interest

What is compound interest and how does it work.

Compound interest is interest calculated on the initial principal as well as the accumulated interest from previous periods. It allows your money to grow faster over time compared to simple interest.

Why is Compound Interest Important for Financial Planning?

Compound interest plays a crucial role in financial planning because it enables individuals to build substantial wealth over the long term. By starting to invest early and allowing investments to compound over time, individuals can take advantage of the power of compounding to achieve their financial goals, such as retirement savings or purchasing a home.

How to Calculate Compound Interest?

The formula for calculating compound interest is:

What Are the Benefits of Compound Interest Investments?

Compound interest investments offer several benefits, including: Faster growth of savings over time Increased wealth accumulation through reinvestment of earnings Diversification opportunities across various asset classes Potential for passive income generation through interest payments or dividends

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RD SHARMA MATHS (ENGLISH) - COMPOUND INTEREST

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• ALGEBRAIC EXPRESSIONS AND IDENTITIES for Class 8 MATHS
• VISUALISING SOLID SHAPES for Class 8 MATHS
• MENSURATION for Class 8 MATHS
• EXPONENTS AND POWERS for Class 8 MATHS
• DIRECT AND INVERSE PROPORTIONS for Class 8 MATHS
• FACTORISATION for Class 8 MATHS
• INTRODUCTION TO GRAPHS for Class 8 MATHS
• PLAYING WITH NUMBERS for Class 8 MATHS

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Case Study Questions for Class 8 Maths

• Last modified on: 9 months ago
• Reading Time: 7 Minutes

Table of Contents

Here in this article, we are providing case study questions for class 8 maths.

Maths Class 8 Chapter List

Latest chapter list (2023-24).

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Data Handling Chapter 5 Squares and Square Roots Chapter 6 Cubes and Cube Roots Chapter 7 Comparing Quantities Chapter 8 Algebraic Expressions and Identities Chapter 9 Mensuration Chapter 10 Exponents and Powers Chapter 11 Direct and Indirect proportions Chapter 12 Factorisation Chapter 13 Introduction to Graphs

Old Chapter List

Chapter 1 Rational Numbers Chapter 2 Linear Equations in One Variable Chapter 3 Understanding Quadrilaterals Chapter 4 Practical Geometry Chapter 5 Data Handling Chapter 6 Squares and Square Roots Chapter 7 Cubes and Cube Roots Chapter 8 Comparing Quantities Chapter 9 Algebraic Expressions and Identities Chapter 10 Visualising Solid Shapes Chapter 11 Mensuration Chapter 12 Exponents and Powers Chapter 13 Direct and Indirect proportions Chapter 14 Factorisation Chapter 15 Introduction to Graphs Chapter 16 Playing with Numbers

Tips for Answering Case Study Questions for Class 8 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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9.CS: Case Study - Exploring Different Sources Of Compound Financing

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The Situation

Quentin is the human resources manager for Lightning Wholesale. Recently, he was approached by Katherine, who is one of the employees in the sporting goods department. She enquired about the possibility of getting an advance on her next paycheck. Quentin informed her that Lightning Wholesale's payroll policy is not to provide advances on paychecks. Katherine indicated that she was having some financial problems, did not have a very good credit rating, and would be forced on her way home to stop in at a payday loan company to take out an advance.

Concerned for his employee, Quentin visited Katherine later in the day and sat down with her to show her the true costs of using a payday loan company. He also wanted to show her a better alternative to get some short-term financing.

Canadian payday loan companies generally operate under one of three structures:

• The Traditional Model. These companies incur all operating costs, provide their own capital for any loan, and collect interest and charges or fees for their services. These companies assume all of the risk.
• The Broker Model. These companies incur all operating costs but do not provide the capital for the loan. A third-party partner provides the capital and the payday loan company charges a brokerage fee for its services. The third-party partner collects all interest and assumes all risk.
• The Insurance Model. These companies incur all operating costs and recover these costs through fees and insurance premiums on the loan. An insurance company (usually owned by the payday loan company) provides all capital and assumes all risk.

The table below summarizes a sample of charges that could be imposed under each model.

• Observe that under Section 347 of the Criminal Code, any charges related to the borrowing of money are considered interest. This includes any types of fees and charges, although in name they may not be called interest.
• As an alternative to using a payday loan company, Katherine could use a finance company that targets people with poor credit ratings or those in quick need of money. These companies typically charge 28% compounded monthly on loans.
• A second alternative is to take a cash advance on her credit card. Most credit card companies charge around 18% compounded daily.

Important Information

• Like most people who borrow money from payday loan companies, Katherine needs to borrow a small sum of money for a short period of time. Her requirements are to borrow $300 for a period of seven days, or one week.
• Assume exactly 52 weeks in a year.
• Convert the effective rate into a nominal weekly compounded rate.
• Calculate the future value of the loan after one week using the weekly periodic rate.
• Calculate any cheque cashing, brokerage, or insurance fees on the future value.
• Take the interest on the loan and add all fees charged, including any flat fees. This is the total interest amount on the loan.
• Convert the interest amount into a percentage of principal. This is the periodic interest rate per week.
• Take the periodic interest rate per week and convert it into a nominal weekly compounded rate.
• Convert the nominal weekly compounded rate into an effective rate.
• Convert both the finance company's interest rate and the credit card's interest rate into effective rates and weekly compounded nominal rates.
• For each option, calculate the future value of her loan and determine the amount of interest charged.
• Examine the effective rates for all of the options. Rank them from the best alternative to the worst alternative.
• Look at the amount of interest paid under the best alternative compared to the worst alternative. Express the worst alternative as a percentage of the best alternative.
• Summarize your findings for Katherine.

Contributors and Attributions

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