Parents: Help your child or teen

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
_Why_Slopes_&_More_Math_1995

More Site Areas 
1.  Solving Linear Equations  2005
2.-Fractions-Rates-Proportns-Units-2006
3.  Algebra, Odds & Ends, HS level-2001
4.-Euclidean-Geometry/Complex No.s 
5.  Analytic Geometry/Functions 2006
6.  Number Theory. 2006-7
7.  Complex Numbers More 2001
8.  Calculus Introduction 2005
More Site Areas 
9   Real  Analysis 1995
10. Secondary IV? maths 2006-7
11. Math Education Essays  2006-7
12. LaTeX2HotEqn: 2004
13. Electric Circuits Etc  2007
14. Quebec Math Education 2004
15-Prequel-to-the-How-TOs-06-2008
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths

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YOU are better than YOU think. Show yourself  how:

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 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

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 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

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Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

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After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;


For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.


Explore collaborative whiteboards from groupboardtwiddla  or scriblink.


Chapter 14 
Compound Interest Calculations
(Compound Growth Calculations)

PS: This chapters uses the compound interest formula to introduce the idea of using formulas directly and indirectly, that is forwards and backwards, and also to introduce and compare arithmetic and algebraic solutions to problems. The ideas here are key to secondary and college level mathematics. Every formula you meet will be used forwards and backwards. And if you understand the algebraic solution method for one formula, you will be able to understand it for all. The first two sections of Chapter 15 shows how to obtain or justify the algebraic formula for solving linear equations ax+b =c for x after several arithmetic examples.  If you understand the algebraic solution methods in this chapter and the next you will, we hope, have a good base for algebra.

To Learn More about compound interest and consumer mathematics (debts, loans, investments, pension plans) see What's in chapters 22 to 35Next

You are now going to meet the compound interest formula. When you meet a formula for the first time, you should wonder what it does or means. You should wonder where it came from or how it was obtained. In this discussion of the compound interest formula, I just want to show you how to use it and how to manipulate or change it to extract other formulas from it. Examples with and without numbers will be given. You should regard the justification or origin of the formula as a problem, one that you should solve by finding an explanation for it.

You need to do more than read and to use formulas as written. You should be able to change them or modify them into another form that might be useful. The authors of mathematics books write for people with this manipulative ability. For such people, modification of formulas as needed is routine.

More Chapter Sections: [14 The Formula] [14 Direct Use] [14 Indirect Use I] [14 Indirect Use II] [14 Further Notes]

1  Compound Interest

When you place (or invest) money in a bank account, a bank pays you money for keeping your money with it, a form of rent for its use of it. The bank is using your money to make loans or investments. The money you are paid is called interest. The amount of interest paid and how often depends on the type of account.

In a compound interest account, a bank adds the interest to your account at the end of a period. This period may be a day, a month, a quarter year, a half-year or a full-year. In each period, all the money in your account is now earning interest. So you now receive interest or rent not only for your original deposit, but also for interest previously added to the account on the completion of each period. Here interest paid at the end of one period will earn interest in future periods. Your money is said to be earning compound interest, or more briefly, compounding.


Postscript: Understanding the Compound Interest Formula

Teachers: Give numerical examples with say i = 5% and P = 1000 dollars (pounds, yen, whatever currency you like, the bigger the better) to show students how or why the formula works. Have them fill-in the following table, or do it for them.

Period
n
Amount at
Start of Period
Amount of Interest Amount at end of Period 103(1.05)n
1 1000 50 1050 1050
2 1050 52.50 1102.50  
3 1102.50      
4        
5        
         
Fill in this table with the aid of a calculator to the nearest penny (two decimal places). Observe the formula use shortens the calculation. Note how the amount at the end of one period becomes the amount at the start of the next.  If you do not like to work with interest calculations, turn this whole chapter into a compound population growth model using the values of  A = P(1+i)n to nearest whole number as an approximation to the whole number of individuals present in the population.

When you place an initial amount P into an account, it is called the principal. In a compound interest account the following happens. The money in your account grows to an amount A after n periods. (The number n here identifies the number of periods your money stays in the account without any withdrawals, or deposits, except for interest payments at the end of each period.) The amount A is given by the compound interest formula
A = P(1+i)n
In this formula, the interest rate per period is given by the quantity i. The formula should only be used when interest is compounded. Again, compounded means the interest is reinvested at the end of each period with no other deposits or withdrawals, Each interest payment deposited in your account then earns interest (rent from the bank) in the following periods.

 

More Chapter Sections: [14 The Formula] [14 Direct Use] [14 Indirect Use I] [14 Indirect Use II] [14 Further Notes]

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  Three Skills for Algebra 
www.whyslopes.com

Foreword, Chapters 
& Appendices 

Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6  Old Language
7  Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I.  Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19  Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning

Real Player Videos

Perfect arithmetic skills with whole numbers & fractions
after or besides chapters 1 to 14.

Arithmetic Videos Summary
Addition with Decimals
Subtraction with Decimals
Multiplication with Decimals
Fraction Arithmetic
Recognizing Primes
Long Division for Decimals
Square Root Simplification
Greatest Common Divisors
Least Common Multiples

Words Before Symbols: 
What is a Variable?
Introduction
Variation between Examples

Variation of Letters

A letter denotes a variable

Cases of Double Variation

Three Notions of a Variable

Constants, Parameters
& Variables

Talking about numbers
Dependent or Independent
Variable, a Matter of Choice

Complex number: starter lesson  

Solving Linear Equations:

A. Letters and Lengths

B. & C. Solving Linear Eq'ns
with stick diagrams.

(i) x + 20 = 29
(ii) 2x + 5 = 20
(iii) 3x + 10 = 32
(iv) 5a + 16 = 3a+ 24

(v)  (½)x + 8 = 24½
(vI)  (¾)a + 16 = (¼)a+ 24
(vii) (¾)q + 17 = 32
(viii) 13 =[2/3]x +7 twice
(x) Animated Examples
(i) Integral Coefficients (A)
(ii) Integral Coefficients (B)
(iii) Fractional Coefficients

(iv) With Parameters

Problem Solving with Linear
Equations in one or many
unknowns, and in essentially 
one unknown - Symbols before
words. 


C. Solving Linear Eq'ns 
without
Stick Diagrams

D. Problems in 
essentially one unknown

E: 2D Systems - Sub Methods.
F. Larger Systems

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Wordy Site Tour:  Not too Bad Vol 2. Foreword 1A Foreword2  Logic Puzzles,  
What is a Variable
  Calculus Starter Guide  Vol 1 Foreword,  
 
 
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