Navigating your
Financial Future
The Joy of Compound Interest
Mary Stinnett
Associate Professor
of Mathematics
Umpqua Community
College
Disclaimers:
• I am a “mathematics educator”
more than a “mathematician”
Math Educator
You invested money in two funds. Last
year, the first fund paid a dividend of
8% and the second a dividend of 5%,
and you received a total of $1330. This
year, the first fund paid 12% dividend
and the second only 2%, and you
received a total of $1500. How much
money did you invest in each fund?
Math Educator
•Simple Interest
• 𝐼 = 𝑃𝑟𝑡
•Compound Interest
•𝐴 = 𝑃 ∙ 1 +
.10 𝑛𝑡
𝑛
•Boring…
Math Educator
• Simple Interest
• How interest is calculated on your
Credit Card
• How to calculate monthly payments
on your car loan
• OR: How much are you paying the
bank in interest for that car loan???
• Rent To Own (ouch!)
Math Educator
• Compound Interest
• Pawn Shops
• Paycheck Loans
• Savings
• Short Term CD
• Retirement Accounts
• College Savings Accounts
Math Educator
• What is “average daily balance”?
• What is the difference between
“APR” and “effective APR”?
• What is an amortization table?
• What if I don’t ask to put my extra
payments “towards principle”, what
could a lending company do with
that money?
Disclaimers:
• I am a “mathematics educator” more than a “mathematician”
• I am NOT a financial planner, nor do I claim
to have the ability to guide anyone
through financial help
Disclaimers:
• I am a “mathematics educator” more than a “mathematician”
• I am NOT a financial planner, nor do I claim to have the ability
to guide anyone through financial help
• I am not up to par on how to cite my
sources “properly” within a PowerPoint
Disclaimers:
• I am a “mathematics educator” more than a “mathematician”
• I am NOT a financial planner, nor do I claim to have the ability
to guide anyone through financial help
• I am not up to par on how to cite my sources “properly”
within a PowerPoint
• I will give you a list of all my resources at
the end of the presentation
Dave Ramsey
• Personal finance is 80 percent behavior,
and only 20 percent head knowledge
Did you know:
About 80 percent of the millionaires in the
United States are first-generation affluent?
“Millionaire Next Door” (Stanley and Danko)
Portrait of a Millionaire:
- Many of the types of businesses we are in
could be classified as dullnormal. We are
welding contractors, auctioneers, rice
farmers, owners of mobile-home parks,
pest controllers, coin and stamp dealers,
and paving contractors.
Portrait of a Millionaire:
- About half of our wives do not work
outside the home. The number-one
occupation for those wives who do work is
teacher.
Portrait of a Millionaire:
- Our household's total annual realized
(taxable) income is $131,000 (median, or
50th percentile)
Portrait of a Millionaire:
- We live well below our means. We wear
inexpensive suits and drive Americanmade cars. Only a minority of us drive the
current-model-year automobile. Only a
minority ever lease our motor vehicles.
Portrait of a Millionaire:
- Most of our wives are planners and
meticulous budgeters.
Think about this…
1. How many people are their in the
world?
7,327,624,830
2. In comparison to the 7-Plus Billion
people in the world, where do you
think your income ranks in
comparison?
Think about this…
3. What is the median household
income in the US? (according to the US
Census)
$50,502
Go to:
www.globalrichlist.com
• Select location: USA (Dollar)
• Enter Annual Net Income: $50,502
Dave Ramsey
Personal finance is 80 percent behavior, and
only 20 percent head knowledge
Thomas Stanley and William
Danko:
About 80 percent of the millionaires in the
United States are first-generation affluent?
Navigating your
Financial Future
The Joy of Compound Interest
Mary Stinnett
Associate Professor of Mathematics
Umpqua Community College
Simple Interest…
• You want to pay off the mortgage to
Boardwalk.
Simple Interest…
• You want to pay off the mortgage to
Boardwalk.
• Mortgage is $200 and interest rate is 10%
• Math = $200 x .10 = $20 mortgage fee
• Total: $200 + $20 = $220
Simple Interest Formula
𝐼 = 𝑃𝑟𝑡
I = Interest
P = Principle (original amount invested or
borrowed)
r = percent interest rate, rewritten as a decimal
t = time, measured in years
Simple Interest Formula
𝐼 = 𝑃𝑟𝑡
Now, to pay off mortgage of Boardwalk
after 2 years….
𝐼 = $200 .10 2
𝐼 = $40
Simple Interest Formula
To pay off mortgage of Boardwalk after 3 years….
𝐼 = 𝑃𝑟𝑡
𝐼 = $200 .10 3
𝑰 = $𝟔𝟎
To pay off mortgage of Boardwalk after 5 years….
𝐼 = 𝑃𝑟𝑡
𝐼 = $200 .10 5
𝑰 = $𝟏𝟎𝟎
To pay off mortgage of Boardwalk after 10 years….
𝐼 = 𝑃𝑟𝑡
𝐼 = $200 .10 10
𝑰 = $𝟏𝟎𝟎𝟎
What is Compound Interest?
Compound interest is interest that is paid on both the
principal and also on any interest from past years…
What does this mean?
After one year, the mortgage pay-off was $220.
What if you had to pay 10% of this $220 instead of the
original $200?
𝐼 = 𝑃𝑟𝑡
𝐼 = $220 .10 1
𝐼 = $22
Making the final payment: $220 + $22 = $242
(compared to the $240 from Simple interest)
And Compound again…
In year three, you would have to pay 10% of the $244…
𝐼 = 𝑃𝑟𝑡
𝐼 = $244 .10 1
𝐼 = $24.40
Making the final payment: $240 + $24.40 =
$264.40
(compared to the $260 from Simple interest)
And Compound again…
Years
Principle
Interest
New
Principle
Simple
Interest
0
1
2
3
$200
$220
$242
$266.20
$20
$22
$24.20
$26.62
$220
$242
$266.20
$292.82
$220
$240
$260
$280
5
$322.10
$32.21
$354.31
$300
10
$518.74
$51.87
$570.62
$400
What do I mean by “Compound
Interest” exactly?
• Take a piece of paper
What do I mean by “Compound
Interest” exactly?
• Take a piece of paper
• Create at Table:
Number of Folds
Number of Layers
0
1
1
2
What do I mean by “Compound
Interest” exactly?
Number of Folds
Number of Layers
0
1
1
2
2
4
3
8
What do I mean by “Compound
Interest” exactly?
Number of Folds
Number of Layers
0
1
1
2
2
4
3
8
4
16
5
32
Number of Folds
Number of Layers
0
1
1
2
2
3
4
4
8
16
5
32
6
64
7
128
8
256
Number of Folds
Number of Layers
For the fun of it…
• https://www.youtube.com/watch?v=kRAEBbotuIE
Compound Interest Rate
• George Washington threw a silver dollar across
the Potomac River in 1776.
• What if Martha took that dollar and invested it
instead. How much would the investment be
worth today?
• 𝐼 = 𝑃𝑟𝑡
• P = Principle = $1
• t = time in years: 2014 – 1776 = 238 years
• r = interest rate: 10% .10
Compound Interest Rate
• George Washington threw a silver dollar across the Potomac
River in 1776. What if Martha took that dollar and invested it
instead. How much would the investment be worth today?
• Simple Interest: 𝐼 = 𝑃𝑟𝑡
• 𝐼 = 1 0.10 (238) = $23.80
• Investment: $1 + $23.80 = $24.80
George Washington’s $1
• Compound Interest
• n = number of times compounded in one year
•𝐴 = 𝑃∙ 1+
.10 𝑛𝑡
𝑛
• When t = 238 years
•𝐴 = 1∙ 1+
0.10 238𝑛
𝑛
George Washington’s $1
• Compound Interest
•𝐴 = 1 ∙ 1 +
0.10 238𝑛
𝑛
Suppose n = 1 (compounded once a year)
𝐴=1∙ 1+
0.10 238𝑥1
=
1
$7,103,000,000
George Washington’s $1
Suppose n = 12 (compounded monthly)
𝐴 =1∙ 1
0.10 (238)(12)
+
=
12
$19,650,740,100
Suppose n = 52 (compounded weekly)
𝐴 =1∙ 1
0.10 (238)(52)
+
=
52
$21,197,406,620
Suppose n = 365 (compounded daily)
𝐴 =1∙ 1
0.10 (238)(365)
+
=
365
$21,616,879,780
George Washington’s $1
y
2E10
1E10
x
5
10
15
20
25
30
George Washington’s $1
y
2E10
1E10
x
50
100
150
200
250
300
350
The number e….
• 𝑒 = lim 1 +
𝑛→∞
1 𝑛
𝑛
≈ 2.71828182845905 …
• Irrational number like π and 2
• First studied by the Swiss mathematician
Leonhard Euler in the 1720s
• Sometimes referred to as the “natural
number”.
The number e….
• 𝑒 = lim 1 +
𝑛→∞
•𝐴 = 𝑃 ∙ 1 +
• 𝐴 = 𝑃𝑒
𝑟𝑡
1 𝑛
𝑛
𝑟 𝑛𝑡
𝑛
George Washington’s $1
• Continuous Compound Interest
• 𝐴 = 𝑃𝑒 𝑟𝑡
(0.10)(238)
• 𝐴 = 1𝑒
=
• $𝟐𝟏, 𝟔𝟖𝟕, 𝟒𝟓𝟖, 𝟗𝟏𝟎
• Compared to Simple Interest:
$24.80
Video…
• https://www.youtube.com/watch?v=hBqZh2suZMM
Compound Interest!!!
• Ben and Arthur were friends who grew up
together. They both knew that they needed to
start thinking about the future.
• At age 19, Ben decided to invest $2,000 every
year for eight years. He picked investment funds
that averaged a 12% interest rate.
Compound Interest!!!
• Ben and Arthur were friends who grew up
together. They both knew that they needed to
start thinking about the future.
• At age 19, Ben decided to invest $2,000 every
year for eight years. He picked investment funds
that averaged a 12% interest rate.
• Then, at age 26, Ben stopped putting money into
his investments. So he put a total of $16,000 into
his investment funds.
Compound Interest!!!
• Now Arthur didn’t start investing until age 27.
• Just like Ben, he put $2,000 into his investment
funds every year until he turned 65.
• He got the same 12% interest rate as Ben, but he
invested 23 more years than Ben did.
• So Arthur invested a total of $78,000 over 39
years.
Compound Interest!!!
• When both Ben and Arthur turned 65,
they decided to compare their
investment accounts.
• Who do you think had more? Ben,
with his total of $16,000 invested
over eight years, or
• Arthur, who invested $78,000 over 39
years?
After 7 years, Ben put out $14000 and
now has $27551
After 7 years, Arthur put out $14000 and
now has $27,551
BUT!!! Ben now has $68,216!!!! And he
did not put in another penny…
Recall, Ben only invested
$16,000
Arthur invested $78,000
Your Dollar!
• When a person invests P dollars into a
retirement account monthly for t years:
•𝐴=𝑃
12
𝑟
1
𝑟 12𝑡
+
12
−1
• Or if it is compounded continuously:
•𝐴 =
𝑃 𝑒 𝑟𝑡 −1
𝑟
𝑒 12 −1
Lottery Dollars Tax on the
Poor?
• Suppose you play $5 a week on the
lottery from the day you are 21
years old into a retirement account
• with average annual return of 15%.
• How much would you have when
you retire at age 65?
Lottery Dollars Tax on the
Poor?
• P = $20 ($5 a week)
• t = 65-21=44 years
• r = 0.15
•𝐴 = 𝑃
12
𝑟
1+
𝑟 12𝑡
12
−1
Lottery Dollars Tax on the
Poor?
• 𝐴 = 20
12
0.15
1+
0.15 (12)(44)
12
•$1,127,407
−1
What about your retirement
goals?
What about your retirement
goals?
Not just Retirement… What
about College Funds?
Not just Retirement… What
about College Funds?
Did you notice…
But 100 BUCKS!!!!
How much does a LARGE coffee and something to eat at
Starbucks cost?
How often do you “grab” something extra at the grocery
store, convenience store, etc.
How much does it cost for a family to go to the movies?
Did you really need that 5-gallon bucket of mayonnaise at
Costco?
How much money could you save smoking a half a pack
instead of one pack of cigarettes a day?
Do you play the lottery?!?
Personal finance is 80 percent
behavior, and only 20 percent
head knowledge
Resources to get you started:
• Local Community College Community Education
Classes
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey (DaveRamsey.Com)
• Financial Peace University
• Legacy Journey
• Foundations in Personal Finance (School
Curriculum)
• Podcast
• Radio Show
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey
• “The Millionaire Next Door” by Stanley and
Danko
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey
• “The Millionaire Next Door” by Stanley and
Danko
• Chris Hogan: Retired Inspired
• https://www.chrishogan360.com/
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey
• “The Millionaire Next Door” by Stanley and
Danko
• Chris Hogan: Retired Inspired
• Financial Planners who have a HEART
OF A TEACHER
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey @ DaveRamsey.com
• “The Millionaire Next Door” by Stanley and
Danko
• Chris Hogan: @ chrishogan360.com
• Financial Planners who have a HEART OF A
TEACHER
• Mary.Stinnett@Umpqua.edu
Resources to get you started:
• Local Community College Community Education
Classes
• Dave Ramsey @ DaveRamsey.com
• “The Millionaire Next Door” by Stanley and
Danko
• Chris Hogan: @ chrishogan360.com
• Financial Planners who have a HEART OF A
TEACHER
• Mary.Stinnett@Umpqua.edu