The Power of Compound Interest: The Good, The Bad, and The Ugly
Albert Einstein, who knew a lot about math, said,
“Compounding interest is the greatest mathematical
discovery of all time.”
Benjamin Franklin, who also had a lot of smarts, said
compounding interest “…is the stone that will turn all
your lead into gold…. Money can beget money, and
its offspring can beget more.”
And, Archimedes said (in ancient Greek because
Archimedes did not speak English), “Give me a lever
and a place to stand and I can move the Earth.” This
is because Archimedes lived before the power of
compound interest was discovered. Otherwise,
Archimedes MIGHT have said,
“Give me a good enough rate on return and some
capital and I can own the Earth.”
The Good: “Compounding – a way to get rich slowly”
Compound interest can make savings grow. The more you save, the more it grows. The
longer you save the more it grows. The higher the rate, the more it grows.
The Bad:
Loans and mortgages – you are using other people’s money, and you have to pay them
for that privilege. The more you borrow, the more you pay. The longer you borrow, the
more you pay.
The Ugly:
Compound interest can also make debt grow. If you do not pay off at least the interest
added each month, you could pay a debt forever and never pay it off. In fact, it could get
bigger and bigger, even if you pay regularly.
Project deadline: Friday, December 7
*Insert any additional papers/printouts directly behind the page they’re related
to.
Name: ______________________
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The Good: How Savings Grow
1. Fred and Ethel are co-workers. Fred is 20 years old, and Ethel is 30. They both receive
a special year-end bonus check for $20,000. Fred tells Ethel that $20,000 is a perfect
retirement next egg and invests it at 10%. Ethel does exactly the same thing. Neither of
them ever adds anything to this investment. If they both retire at age 65,
a. write an exponential model to describe how much each of their investments are
worth (M) at age t.
Fred:
Ethel:
_____________________ (1 pt)
_____________________ (1 pt)
b. Use the exponential models from part a to calculate how much money each will
have at retirement. (You must show your work.)
Fred:
_________________________________ (1 pt)
Ethel:
_________________________________ (1 pt)
c. Make an Excel spreadsheet organizing the financial information for each of them.
You should have a column for the age of Fred/Ethel and a column for the value of
their investment at that age. You should use formula(s) to calculate the amount
of the investment. Attach your spreadsheet and a copy of your spreadsheet which
shows the formulas you used (Tools: Options: check the Formulas box). A part of
the spreadsheet is shown below. (3 pts)
Fred's
Amount
Fred's Age
20
21
22
23
24
25
26
Ethel's Age Ethel's Amount
20000
30
20000
22000
31
22000
24200
32
24200
26620
33
26620
29282
34
29282
32210.2
35
32210.2
35431.22
36
35431.22
d. Pretend that your parents put $________ in a savings account when you were born
that was earning 4% APR compounded quarterly for 18 years. Create (and print) a
spreadsheet and the formula sheet that could be used to find the total amount of money
in the account at the end of 18 years. (3 pts)
2. Your parents have saved $100 a month at 8% APR to prepare for your college education.
(That means, every month you’re adding another $100 to the pool of money; an annuity
is regular savings.) Make an Excel spreadsheet that will help you figure out how much
money you will have to spend on your college education. Also, print the formulas for
this spreadsheet. (3 pts)
_____________
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3. A. Find the approximate total cost of attending a college you’re interested in for four
years (or more if you’re planning on seeking a higher degree). Cite your source(s). (2
pts)
Name of College/University: ______________
Tuition
Room/Board
Transportation
__________
__________
_____
_____
_____
_____
_____
Total
_____
Source: ____________________________
B. Write an equation which can be solved to find out how much money your parents would
have had to put in an account when you were born at 8% interest, compounded
monthly, to have enough money at age 18. (1 pt)
C. Solve the equation in part B. Show all work. (1 pt)
D. Write and solve an equation which will find how many years it would take to double
and investment of $100,000 if interest is compounded quarterly at 6%. (Use
logarithms) (1 pt)
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The Bad: Loans and Mortgages
While compound interest can make your savings grow, it also makes long-term loans cost more
than short-term loans. The following formula can be used to calculate the monthly payment
(M) for a loan:
[ P(1  r )12 y r ]
M=
(1  r )12 y  1
where P = principal, r = MONTHLY interest rate,
y = number of years of the loan.
4. Suppose you want to buy a house. You have a down payment but need to finance $100,000
to buy the house. Your bank offers you the following terms compounded monthly.
$100,000 at 6.5% APR for 30 years
-or-
$100,000 at 7% APR for 15 years
A. What would be the monthly payment on each loan? (Show your work.) (1 pt ea)
_____________________
____________________
B. What is the total cost over the life of the loan for each offer? (Show your work.) (1 pt each)
_____________________
____________________
C. Which loan is more expensive in the long run? (1 pt)
_____________________
D. How much more expensive? (1 pt)
_____________________
E. Discuss the benefits and drawbacks of EACH loan. Which do you think is the better deal?
Why? (3 pts)
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
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The Ugly: Carrying Credit Card Debt
5. Don Dumbfounded received an Express credit card upon graduation. The big splash print
on the front said "Introductory low interest rate of 3%". When he started college in September,
Don used the credit card to buy a stereo for his dorm room for $2000. Since he was a student
and only working part time for near minimum wage, Don paid the minimum acceptable
amount of $10 on his credit card each month. He never charged anything to that card again.
Later, he discovered the terms of the credit card in small print on the back that said the 3%
intro rate was for the months of June, July, and August of the first year only. Thereafter, all
charges would be at the standard rate of 16%.
A. Don graduated from college, a full FIVE years after starting. Create an Excel spreadsheet
to figure out how much he owed on that $2000 stereo. A part of a sample spreadsheet is
shown below. (1 pt)
_____________________
Month
1
2
3
Amount Paid
10
10
10
60
10
Amount Owed
2016.67
2033.56
2050.67
B. How much money had Don paid to the credit card company? (1 pt)
____________
C. Don did not find a very good job after graduation, so he continued to make only the
minimum $10/month payment on that credit card. Expand your spreadsheet to find what
John owed ten years after buying the stereo. (1 pt)
_____________________
D. How much had Don paid the company after 10 years? (1 pt)
____________
E. When he retired, 40 years after graduation and 45 years after first buying the stereo, Don
was still making those $10 minimum payments. Expand your spreadsheet to find out what he
owed then. Print just the first and last pages of your spreadsheet. Also print the formulas for
the first page. (3 pts)
_____________________
F. What had he paid the company by then? (1 pt)
____________
G. Why did Don's debt grow even though he was making a monthly payment? (1 pt)
___________________________________________________________
___________________________________________________________
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H. Sally Smart also got the same credit card and bought the same stereo. But, Sally also knew
about compound interest and how it works. She calculated the interest on the credit card debt
for the first year, which is ______________, and divided it by 12 to find the minimum
monthly payment ______________ in order to keep the $2000 debt from growing. (Show
all work.) (2 pts)
I. Research: Find two ways that laws have recently changed in order to help prevent people
from getting into serious financial trouble with credit cards. Cite your source(s). (2 pts)
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
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