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 identify, put into words, a unifying
theme for teen and adult education in mathematics & science. 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.
If you understand the
algebraic solution methods in this chapter and the next you will, and in the
site area site folder Solving
Linear Equations 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 35 Next
Teachers & Tutors: The theme forward and backward use of
formulas is expanded in full, or nearly so, in the Algebra
teaching & TutoringHow-TOs.
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
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]
| |
Three Skills
For
Algebra
understanding & explaining
Reason and Math
Volume 2
Printed in Canada
ISBN 0-9697564-2-9
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Chapters and Appendices
Home
Postscript: The 4-th Skill For Algebra
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
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
|