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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
Chapter 24
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Second, imagine that John has asked the A1Z26 Pension Provider Company to let him debit $1.00 from his pension plan the end of each month for the next 15 years, at the interest rate of 4 percent compounded monthly. We will calculate the amount of debt that the payments represent at the end of fifteen years, and then see what amount of credit is then required to cancel this debt.
1. At the end of the first month, the first payment of $1.00 to John
represents a debt which grows at 4 percent, compounded monthly for 180-1 =179
months. This contributes a debt of $1.00(1+[.04/12])179 =
(1+[.04/12])179 dollars.
2. At the end of the second month, the second payment of $1.00 to John
represents a debt which grows at 4 percent, compounded monthly for 180-2 =178
months. This contributes a debt of $1.00(1+[.04/12])178 =
(1+[.04/12])178 dollars.
3. At the end of the third month, the third payment of $1.00 to John
represents a debt which grows at 4 percent, compounded monthly for 180-3 =177
months. This contributes a debt of $1.00(1+[.04/12])177 =
(1+[.04/12])177 dollars.
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Now at the end of fifteen years, a deposit of 3,500,000 dollars today will leave John with a credit of 637105.57 dollars. Observe
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This suggests that the A1Z26 Pension Plan Company would be willing to sell John fifteen years of monthly payments of 2588.91 dollars (approximately) in exchange for the amount of 350000 dollars at their announced 4% cent interest rate.
Second Solution: Suppose John want to receives a payment of 1.00 dollar at the end of each month for the next fifteen years = 180 months. Recall that a deposit of P = [(A)/((1+i)n)] will grow the amount A at the end of n periods in a compound interest account. Suppose John want to receives a payment of 1.00 dollar at the end of each month for the next fifteen years = 180 months from a compound interest account, paying 4 percent compounded monthly. What does he need today in the account today to be able to make all the withdrawals?
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Note in computing, rounding should be done last and avoided in intermediate calculations for the sake of preserving accuracy. (The above calculation would be slightly less accurate if the intermediate result 135.192188 was rounded to 135.19 dollars.)
More Chapter Sections:
Next Chapter: 25 Inductive Proofs and Recursive
Definitions
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2. Three Skills for AlgebraForeword, 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 lessonSolving 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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