2. Managing Your Money
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3. 4A Discussion Questions
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.
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4. The Power of Compounding
Unit 4B: Part 1
The Power of Compounding
King Edward’s debt after 535 years….
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5. Simple Vs. Compound Interest
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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6. Definitions
The principal in financial formulas is the balance upon which interest is paid.
Simple interest is interest paid only on the original principal, and not on any interest added at later dates.
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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7. CN (1-2) Savings Bond
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
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8. Brief Review: Powers and Roots CN (3-6)
Basic Powers
Power Rules
Basics of Roots
Roots as Fractional Powers
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9. The Compound Interest Formula CN (7)
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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10. Compound Interest Formula for Interest Paid Once a Year
A = accumulated balance after Y years
P = starting principal
APR = annual percentage rate (as a decimal)
Y = number of years
Make sure students remember to make the APR a decimal and that they understand how to solve for both A as well as P.
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11. 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.
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12. Results
Overall, the account paying compound interest builds to $ while the simple interest account reaches only $150, even though both pay at the same 10% rate.
The basic point:
For the same interest rate, compound interest is always better for the investor than simple interest.
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13. Standard Calculators CN (8) Excel File
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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14. Compound Interest as Exponential Growth
The New College case demonstrates the remarkable way in which money can grow with compound interest.
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.
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15. New College Debt at 2% CN (9-10)
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.
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16. Mattress Investments CN (11)
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),
11. How much would it be worth now?
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17. 4B Part 1 Homework: P.224: Review Questions 1-8
P.224: Does it make sense : 9-14
P.224 Basic Skills: 15-42
P.224 Simple Interest: odd
Class Notes: 1-11
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18. 4B Part 2: p.216 Compound Interest paid more than once a year
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19. Definitions Present value is the original principal.
Future value is the accumulated amount.
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20. Compound Interest Formula for Interest Paid n Times per Year
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
Make sure students remember to make the APR a decimal and that they understand how to solve for both A as well as P.
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21. Compound Interest
Show how quarterly compounding affects a $1000 investment at 8% per year.
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22. Definition
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 =
absolute increase
starting principal
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23. 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
Submit to students that perhaps two reasons that we should understand the differences between the two percentages are 1) to be able to compare fairly two different savings institutions and their rates, and 2) to know which is the rate of calculation so we do not use APY erroneously in our formula projections.
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24. Continuous Compounding
Show how different compounding periods affect the APY for an APR of 8%.
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25. Continuous Compounding
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26. Compound Interest Formula for Continuous Compounding
A = accumulated balance after Y years
P = starting principal
APR = annual percentage rate (as a decimal)
Y = number of years
= a special irrational number with a value of
It might be pointed out to students that, in addition to the natural sciences, we sometimes use this continuous model in business calculus due to its brevity and ease of differentiating and integrating. Similar calculations can be obtained with the previous compound interest formula by simply making n get very large.
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