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Managing Your Money
Copyright © 2011 Pearson Education, Inc.
4A Discussion
Questions
1.
2.
3.
How do you feel about the homeowner’s total percentage
mentioned in #2 of the Analysis? What do financial
experts recommend?
How do you feel about the total vehicle percentage in #3
of the Analysis? How would you find the line between
affordable and not affordable in terms of a vehicle?
Reflect on the personal impressions you put together the
Davidson’s original budget and how this activity might
impact your future financial decisions.
Copyright © 2011 Pearson Education, Inc.
Unit 4B: Part 1
The Power of
Compounding
King Edward’s debt after 535 years….
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Slide 4-4
Simple Vs. Compound Interest
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Honest John’s Money Holding Service
Pays 5% interest each year
You deposit $1000
Over 3 years you receive simple interest of ____
Only paid on principal of ______
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Slide 4-5
4-B
Definitions
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The principal in financial formulas is the balance
upon which interest is paid.
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Simple interest is interest paid only on the
original principal, and not on any interest added at
later dates.
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Compound interest is interest paid on both the
original principal and on all interest that has been
added to the original principal.
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Slide 4-6
CN (1-2)
Savings Bond
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4-B
While banks almost always pay compound
interest, bonds usually pay simple interest.
Suppose you invest $1000 in a savings bond that
pays simple interest of 10% per year.
1. How much total interest will you receive in 5
years?
2. If the bond paid compound interest would your
receive more or less total interest? Explain
Copyright © 2011 Pearson Education, Inc.
Slide 4-7
Brief Review: Powers and Roots
CN (3-6)
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4-B
Basic Powers
Power Rules
Basics of Roots
Roots as Fractional Powers
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Slide 4-8
The Compound Interest Formula
CN (7)
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4-B
King Edward’s debt to the New College….
He borrowed $224
Put into an interest-bearing account for 535 years
4% per year
The balance at the end of 1 year is _____
The balance at the at the end of 2 years is ____
The balance at the end of 3 years is ______
7. Continue pattern, write the formula and the balance
after 10 years:
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Slide 4-9
4-B
Compound Interest Formula
for Interest Paid Once a Year
A  P  (1  APR )
Y
A = accumulated balance after Y years
P = starting principal
APR = annual percentage rate (as a decimal)
Y = number of years
Copyright © 2011 Pearson Education, Inc.
Slide 4-10
4-B
Simple and Compound Interest
Compare the growth in a $100 investment for
5 years at 10% simple interest per year and at
10% interest compounded annually.
The compound interest account earns $11.05 more
than the simple interest account.
Copyright © 2011 Pearson Education, Inc.
Slide 4-11
4-B
Results
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Overall, the account paying compound interest
builds to $161.05 while the simple interest
account reaches only $150, even though both pay
at the same 10% rate.
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The basic point:
For the same interest rate, compound interest is
always better for the investor than simple interest.
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Copyright © 2011 Pearson Education, Inc.
Slide 4-12
Standard Calculators CN (8)
Excel File
4-B
Standard Calculators: You can do compound
interest calculations on any calculator that has
key for raising numbers to powers
 The only “trick” is making sure you follow the
standard order of operations
8. Do practice problem in a calculator
 The built in function FV (for future value) makes it
easy to do compound interest calculations using
Excel.
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Copyright © 2011 Pearson Education, Inc.
Slide 4-13
4-B
Compound Interest as Exponential Growth
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The New College case demonstrates the
remarkable way in which money can grow with
compound interest.
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Note that while the value rises slowly at first, it
rapidly accelerates, so in later years the value
grows by much more each year than it did during
earlier years.
Copyright © 2011 Pearson Education, Inc.
Slide 4-14
4-B
New College Debt at 2%
CN (9-10)
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If the interest rate is 2%, calculate the amount due
to New College using:
9. Simple interest
10. Compound interest
Effects of Interest Rate Changes…
You should note the remarkable effects of
small changes in the compound interest rate.
Copyright © 2011 Pearson Education, Inc.
Slide 4-15
Mattress Investments
CN (11)
4-B
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Your grandfather put $100 under his mattress 50
years ago. If he had instead invested it in a bank
account paying 3.5% interest compounded yearly
(roughly the average US rate of inflation during
that period),
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11. How much would it be worth now?
Copyright © 2011 Pearson Education, Inc.
Slide 4-16
4-B
4B Part 1 Homework:
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P.224: Review Questions 1-8
P.224: Does it make sense : 9-14
P.224 Basic Skills: 15-42
P.224 Simple Interest: 43-53 odd
Class Notes: 1-11
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Slide 4-17
4-B
4B Part 2: p.216
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Compound Interest paid more than once a year
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Slide 4-18
4-B
Definitions
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Present value is the original principal.
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Future value is the accumulated amount.
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Slide 4-19
4-B
Compound Interest Formula
for Interest Paid n Times per Year
 APR 
A  P 1 
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n 
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( nY )
A = accumulated balance after Y years
P = starting principal
APR = annual percentage rate (as a decimal)
n = number of compounding periods per year
Y = number of years
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Slide 4-20
4-B
Compound Interest
Show how quarterly compounding affects a $1000
investment at 8% per year.
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Slide 4-21
4-B
Definition
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The annual percentage yield (APY) is the actual
percentage by which a balance increases in one
year. It is sometimes also called the effective yield
or simply the yield.
APY = relative increase =
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absolute increase
starting principal
Slide 4-22
4-B
APR vs. APY
APR = annual percentage rate
APY = annual percentage yield
APY = APR if interest is compounded annually
APY > APR if interest is compounded more than
once a year
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Slide 4-23
4-B
Continuous Compounding
Show how different compounding periods affect the
APY for an APR of 8%.
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Slide 4-24
4-B
Continuous Compounding
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Slide 4-25
4-B
Compound Interest Formula
for Continuous Compounding
A  Pe
( APRY )
A = accumulated balance after Y years
P = starting principal
APR = annual percentage rate (as a decimal)
Y = number of years
e = a special irrational number with a value
of e  2.71828
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Slide 4-26