# 9.10: Exercise - Mathematics

## Skills

1. A friend lends you $200 for a week, which you agree to repay with 5% one-time interest. How much will you have to repay? 1. Suppose you obtain a$3,000 T-note with a 3% annual rate, paid quarterly, with maturity in 5 years. How much interest will you earn?
1. A T-bill is a type of bond that is sold at a discount over the face value. For example, suppose you buy a 13-week T-bill with a face value of $10,000 for$9,800. This means that in 13 weeks, the government will give you the face value, earning you $200. What annual interest rate have you earned? 1. Suppose you are looking to buy a$5000 face value 26-week T-bill. If you want to earn at least 1% annual interest, what is the most you should pay for the T-bill?
1. You deposit $300 in an account earning 5% interest compounded annually. How much will you have in the account in 10 years? 1. How much will$1000 deposited in an account earning 7% interest compounded annually be worth in 20 years?
1. You deposit $2000 in an account earning 3% interest compounded monthly. 1. How much will you have in the account in 20 years? 2. How much interest will you earn? 1. You deposit$10,000 in an account earning 4% interest compounded monthly.
1. How much will you have in the account in 25 years?
2. How much interest will you earn?
1. How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. 1. How much would you need to deposit in an account now in order to have$20,000 in the account in 4 years? Assume the account earns 5% interest.
1. You deposit $200 each month into an account earning 3% interest compounded monthly. 1. How much will you have in the account in 30 years? 2. How much total money will you put into the account? 3. How much total interest will you earn? 1. You deposit$1000 each year into an account earning 8% compounded annually.
1. How much will you have in the account in 10 years?
2. How much total money will you put into the account?
3. How much total interest will you earn?
1. Jose has determined he needs to have $800,000 for retirement in 30 years. His account earns 6% interest. 1. How much would he need to deposit in the account each month? 2. How much total money will he put into the account? 3. How much total interest will he earn? 1. You wish to have$3000 in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying 8% compounded quarterly?
1. You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest. 1. How much do you need in your account at the beginning 2. How much total money will you pull out of the account? 3. How much of that money is interest? 1. How much money will I need to have at retirement so I can withdraw$60,000 a year for 20 years from an account earning 8% compounded annually?
1. How much do you need in your account at the beginning
2. How much total money will you pull out of the account?
3. How much of that money is interest?
1. You have $500,000 saved for retirement. Your account earns 6% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years? 1. Loren already knows that he will have$500,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 10% interest, how much could the annuity provide each month?
1. You can afford a $700 per month mortgage payment. You’ve found a 30 year loan at 5% interest. 1. How big of a loan can you afford? 2. How much total money will you pay the loan company? 3. How much of that money is interest? 1. Marie can afford a$250 per month car payment. She’s found a 5 year loan at 7% interest.
1. How expensive of a car can she afford?
2. How much total money will she pay the loan company?
3. How much of that money is interest?
1. You want to buy a $25,000 car. The company is offering a 2% interest rate for 48 months (4 years). What will your monthly payments be? 1. You decide finance a$12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest will you pay over the life of the loan?
1. You want to buy a $200,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. 1. How much is the loan amount going to be? 2. What will your monthly payments be if the interest rate is 5%? 3. What will your monthly payments be if the interest rate is 6%? 1. Lynn bought a$300,000 house, paying 10% down, and financing the rest at 6% interest for 30 years.
1. Find her monthly payments.
2. How much interest will she pay over the life of the loan?
1. Emile bought a car for $24,000 three years ago. The loan had a 5 year term at 3% interest rate, making monthly payments. How much does he still owe on the car? 1. A friend bought a house 15 years ago, taking out a$120,000 mortgage at 6% for 30 years, making monthly payments. How much does she still owe on the mortgage?
1. Pat deposits $6,000 into an account earning 4% compounded monthly. How long will it take the account to grow to$10,000?
1. Kay is saving $200 a month into an account earning 5% interest. How long will it take her to save$20,000?
1. James has $3,000 in credit card debt, which charges 14% interest. How long will it take to pay off the card if he makes the minimum payment of$60 a month?
1. Chris has saved $200,000 for retirement, and it is in an account earning 6% interest. If she withdraws$3,000 a month, how long will the money last?

## Concepts

1. Suppose you invest $50 a month for 5 years into an account earning 8% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 25 years. How much will you have in the end? 1. Suppose you put off making investments for the first 5 years, and instead made deposits of$50 a month for 25 years into an account earning 8% compounded monthly. How much will you have in the end?
1. Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal? 1. Kendra wants to be able to make withdrawals of$60,000 a year for 30 years after retiring in 35 years. How much will she have to save each year up until retirement if her account earns 7% interest?
2. You have $2,000 to invest, and want it to grow to$3,000 in two years. What interest rate would you need to find to make this possible?
1. You have $5,000 to invest, and want it to grow to$20,000 in ten years. What interest rate would you need to find to make this possible?
1. You plan to save $600 a month for the next 30 years for retirement. What interest rate would you need to have$1,000,000 at retirement?
1. You really want to buy a used car for $11,000, but can only afford$200 a month. What interest rate would you need to find to be able to afford the car, assuming the loan is for 60 months?

## Exploration

1. Pay day loans are short term loans that you take out against future paychecks: The company advances you money against a future paycheck. Either visit a pay day loan company, or look one up online. Be forewarned that many companies do not make their fees obvious, so you might need to do some digging or look at several companies.
1. Explain the general method by which the loan works.
2. We will assume that we need to borrow $500 and that we will pay back the loan in 14 days. Determine the total amount that you would need to pay back and the effective loan rate. The effective loan rate is the percentage of the original loan amount that you pay back. It is not the same as the APR (annual rate) that is probably published. 3. If you cannot pay back the loan after 14 days, you will need to get an extension for another 14 days. Determine the fees for an extension, determine the total amount you will be paying for the now 28 day loan, and compute the effective loan rate. 1. Suppose that 10 years ago you bought a home for$110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
1. Let's consider your existing mortgage:
1. How much money did you pay as your down payment?
2. How much money was your mortgage (loan) for?
3. What is your current monthly payment?
4. How much total interest will you pay over the life of the loan?
1. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house is now valued at$150,000.

How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)

1. How much money have you paid to the loan company so far?
2. How much interest have you paid so far?
3. How much equity do you have in your home (equity is value minus remaining debt)
1. Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate.
1. If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?
2. How much interest will you pay over the life of the new loan?
1. Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total.
1. How much will you save each month because of the lower monthly payment?
2. How much total interest will you be paying (you need to consider the amount from 2c and 3b)
3. Does it make sense to refinance? (there isn't a correct answer to this question. Just give your opinion and your reason)

## Logic-Math Exercises for Children

The Logic-Math books are designed to develop critical-thinking skills in children through exercises involving math concepts. Some of these concepts are customarily introduced to this age group others are typically reserved for older children. However, their introduction in these books is done in a fun and age-appropriate manner. These concepts include number signs, counting, addition, subtraction, multiplication, division, fractions, decimals, percent, graphs, geometry, volume, and more, as well as number concepts that are involved in such topics as time and money.

The exercises involve organizing information, sequencing, pattern decoding, understanding relationships, inferring, solving analogies, and deducing, all presented in a format designed to appeal to young children. The first two books in the series are for students in grades K-2. Many of the lessons are pictorial, with simple instructions that can be read to pre-literate children. The third book takes the series to a more advanced level and is for children in grades 3-4. All of the books include exercises in a range of challenge levels that will enable children to experience both success and the struggle that makes success more satisfying. Children of all ability levels will enjoy the challenges in these books and will soon be applying their critical-thinking skills to other areas of learning and life.

The Logic-Math books are designed to develop critical-thinking skills in children through exercises involving math concepts. Some of these concepts are customarily introduced to this age group others are typically reserved for older children. However, their introduction in these books is done in a fun and age-appropriate manner. These concepts include number signs, counting, addition, subtraction, multiplication, division, fractions, decimals, percent, graphs, geometry, volume, and more, as well as number concepts that are involved in such topics as time and money.

The exercises involve organizing information, sequencing, pattern decoding, understanding relationships, inferring, solving analogies, and deducing, all presented in a format designed to appeal to young children. The first two books in the series are for students in grades K-2. Many of the lessons are pictorial, with simple instructions that can be read to pre-literate children. The third book takes the series to a more advanced level and is for children in grades 3-4. All of the books include exercises in a range of challenge levels that will enable children to experience both success and the struggle that makes success more satisfying. Children of all ability levels will enjoy the challenges in these books and will soon be applying their critical-thinking skills to other areas of learning and life.

## How to help at home

You don’t need to be an expert to support your child with maths or help them develop a good sense of number! Here are three simple but effective learning ideas that you can try with your child at home.

### 1. Dice with decimals

Make ‘×’ ‘÷’ and ‘10’, ‘100’, ‘1000’ cards to place face down in two piles. Roll a dice four times to create a number (e.g. 4258), then insert a decimal point somewhere (e.g. 42.58). Take a card from each pile and do the calculation (e.g. 42.58 ÷ 100 = 0.4258).

### 2. Play Battleship games

Play Battleships by drawing ships on coordinate grids. Try to sink each other’s ships by guessing their positions using coordinates, such as (1,2). Remember that the first number in the coordinate bracket is on the horizontal x-axis. The second number is on the vertical y-axis.

### 3. Hit the sales

Sales in shops, catalogues or online are great for working with percentages. For example, in a 20% off sale, if the full price (that is 100%) of an item is £10, how much is the item discounted by (£2) and what will the sale price be (£8)?

Each category has many resources within so why not jump in and explore the site?

### Popular Resources

Have a look at some of our popular resources in this category.

Year 5 Assessment Paper. Please note these are not intended to be used as a set of written questions where the child answers on paper in silence. The questions should be presented over a period of several days. Encouraging discussion of the questions will give a much greater insight into the child's understanding.

Solve multi-step problems and check by carrying out inverse operations.

Find the number from the clues given.

Solving problems involving Ɖ for 2 voucher offer.

Answers for the Year 5 assessment paper.

Some of the questions are quite long, but they can be answered with a single step operation.

Much trickier questions as they all need more than one step to reach the right answer.

## CBSE Math - Additional Practice Questions | NCERT Solutions

Additional practice questions with video explanations for each chapter covered in the NCERT syllabus for class 8, class 9, class 10, and class 11. These include a mix of questions that help consolidate concepts and those that help build intuition for higher order thinking.

Also includes solutions to exercise questions for each chapter. Video solution to past year CBSE class X math board papers have also been provided.

## Class 9 - Maths

Get NCERT solutions for Class 9 Maths free with videos of each and every exercise question and examples. All answers are solved step by step with videos of every question.

### Topics include

1. Chapter 1 Number systems - What are Rational, Irrational, Real numbers, Law of Exponents, Expressing numbers in p/q form, Finding rational number between two numbers , Number line
2. Chapter 2 Polynomials- Degrees, zeroes of polynomial, Remainder Theorem, Factorization - Splitting middle term, Factor Theorem, Algebraic Identity
3. Chapter 3 Coordinate Geometry - Cartesian System, Abscissa Ordinate, Quadrant, Plotting points (x,y)
4. Chapter 4 Linear Equations in Two Variables - Solution - Unique, Infinitely Many , Graph of linear equation in two variables, Forming equations, Equation of lines parallel to x-axis, y-axis
5. Chapter 5 Introduction to Euclid's Geometry - Euclid's Definitions, Axioms , Postulates, Equivalent versions of Euclid's Fifth Postulate
6. Chapter 6 Lines and Angles - Complementary Angles, Supplementary Angles, Adjacent Angles, Vertically Opposite Angles, Linear pair, Alternate interior angles, interior angles on same side of transversal is supplementary, Sum of angles of a triangle is 180, Exterior Angle is sum of interior opposite angle, Theorems.
7. Chapter 7 Triangles - Criteria of Congruence of Triangles - ASA, AAS, SSS, RHS, Angle opposite to equal sides of isosceles triangle are equal, Side opposite to greater angle is longer, Angle opposite to greater side is larger, Theorems
8. Chapter 8 Quadrilaterals - Angle sum property of quadrilateral, Properties of Paralleogram, Theorems, Conditions for quadrilateral to be a parallelogram, Mid-point theorem
9. Chapter 9 Areas of parallelograms andtriangles - Figures on the same base and between the same parallels,
10. Chapter 10 Circles - Terms - Chord, arc, Sector, Segment, Angle subtended by chord at a point, perpendicular from centre to the chord, circle throught 3 points, equal chords and their distances from centre, angle subtended by an arc of the circle.
11. Chapter 11 Constructions - We learn how to draw a bisector of an angle, how to draw a perpendicular bisector of a line (with justification), and then we learn how to draw angles using compass like 60, 45, 90. We also study how to do construct a triangle when perimeter and 2 base angles are given sum of sides, base, and angle is given difference of sides, base and angle is given
12. Chapter 12 Heron's Formula - Area of triangle by herons formula, Finding area of quadrilateral by heros formula
13. Chapter 13 Surface Areas and Volumes - Curved , total surface area, volume of cuboid, cube, cylinder, right circular cone, sphere, hemisphere
14. Chapter 14 Statistics - Primary, Secondary data, raw, ungrouped, grouped frequency distribution table, Graphical Representation - Bar graph, Histogram, Frequency Polygon, Mean, median, mode.
15. Chapter 15 Probability - Experiment, Probability lies between 0 & 1, Empirical (Experimental) Probability of event is number of trials where E has happened by total number of trials.

Each chapter is divided into 2 parts - Concept Wise, and Serial Order Wise.

In Serial Order Wise, you can check the chapter according to the NCERT Book. The chapter is divided into Exercises and Examples. You can check out a question by clicking on the exercise link

This is useful if you want the solution of a specific question.

There is a better way to do the chapter.

In Concept Wise, we have divided the chapter into concepts. First the concept is taught, then the questions of that concept are solved - from easy to difficult. This is the Teachoo way of learning.

Click on a chapter and start doing.

Note: When you click on a link from a chapter. The first question or topic will open. To see other questions, there is a list with arrows which has all the questions.

## Times tables worksheets

Would you like to practise your tables at your leisure? Below you will find tables practise worksheets. Click on one of the worksheets to view and print the table practise worksheets, then of course you can choose another worksheet. You can choose between three different sorts of exercises per worksheet. In the first exercise you have to draw a line from the sum to the correct answer. In the second exercise you have to enter the missing number to complete the sum correctly. In the third exercise you have to answer the sums which are shown in random order. All in all, three fun ways of practising the tables in your own time, giving you a good foundation for ultimately mastering all of the tables. Choose a table to view the worksheet.

## What is Math Enrichment?

The IMACS Live! Math Enrichment program is perfect for above average to gifted elementary school and middle school students. Whether your child excels at math and is ready for greater challenges, has lost their excitement for math, or seems indifferent to math, IMACS Live! can help them REACH their full potential. Our program introduces students to advanced mathematical concepts in an interesting and engaging way. Our students learn sophisticated math skills, prepare for middle and high school, and most importantly have fun!

## Free Worksheets on Percentage

Worksheets are probably the best way to gauge a child’s understanding of a particular topic. They are also a good way to give kids some practice!

Whether you are a homeschooling parent or a teacher, percentage worksheets are an invaluable resource. Free and printable, these worksheets are easily available online. From worksheets with simple problems that help the kids master the basics to more complex and advanced percentage word problems, there are worksheets with varying levels of difficulty.

As with most math topics, percentage is also a concept that kids may need to use often in real life. It is a good idea to relate their learning of this concept with real-life examples and situations. The more interactive and engaging the learning process, the better. Once they have understood the basics, hand over these worksheets to them and see how much they enjoy the subject!