Dr. Antonio Quesada – Director, Project AMP
Project AMP
Savings, Loans, and Interest Rate
Lesson Lab Summary
by Barbara Adler, Firestone High School, Akron
Scott Waseman, Barberton High School, Barberton
Subject:
Algebra 1, Algebra 2
Grade:
9th, 10th
Topic:
Savings, Loans, and Interest Rate
Strands:
Number and Numeracy
Algebra and Functions
Mathematical Processes
Objectives:
Strand: Number and Numeracy
• Estimate and compute with real numbers.
• Apply rates, ratios, proportions, and percents.
Strand: Algebra and Functions
• Represent a mathematical relationship using a table, graph, symbols, and
words, and describe how a change in the value of one variable affects the
value of a related variable.
Strand: Mathematical Processes
• Communicate mathematical ideas, reasoning, and solutions through the
use of appropriate mathematical terminology, notations, symbols,
definitions, models, and other representations.
Materials:
spreadsheet software, internet access, printer, and worksheets
Expected time: 2 or 3 class periodsSavings, Loans, and Interest Rate
Lesson Lab Plan
by Barbara Adler, Firestone High School, Akron
Scott Waseman, Barberton High School, Barberton
Concepts/ Learning and Ohio Proficiency Objectives
Number and Numeracy
2. Estimate and compute with real numbers.
3. Apply rates, ratios, proportions, and percents.
Algebra and Functions
6. Represent a mathematical relationship using a table, graph, symbols, and
words, and describe how a change in the value of one variable affects the value of a
related variable.
Mathematical Processes
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Dr. Antonio Quesada – Director, Project AMP
15. Communicate mathematical ideas, reasoning, and solutions through the use
of appropriate mathematical terminology, notations, symbols, definitions, models, and
other representations.
Task Overview
Students will use the real life situations of saving money and repaying loans to learn
the importance of interest rate and compound interest in consumer applications.
The focus is for students to gain an understanding of how savings, interest, and time
are related. There is a direct relationship between interest rates and savings over time.
Prior knowledge:
Students know how to write a percentage rate as a decimal, eg, 8.5% = .085
Students are familiar with basic spreadsheets: how to enter a formula, fill it down a
column, and make a spreadsheet chart.
After the teacher introduces this exciting topic (below), students complete these tasks:
1. When you save regularly over time, compound interest works for you.
• Compare how long it takes to save $100,000, given several interest rates.
• Explore how much has to be saved each week, given several interest rates, to save
at least $1,000,000 over a working life.
2. When you borrow money, compound interest works against you.
• Given the term of a loan, find the monthly payment.
• Given the amount you want to pay each month, find how long you will pay.
Student pairs will complete the worksheets and discuss their findings.
The teacher acts as a facilitator while students are completing the activities. This work
is planned for two 50-min classes. At the end of the second class or start of the next
class, the teacher will summarize and reinforce the conceptual ideas for the activities.
Integration Learning Strategies
1. Teacher introduction.
Asking, “Who wants to be a millionaire? without being a superstar or winning the
lottery”, the teacher will introduce the goal of saving a substantial sum, given
regular savings and time.
Use the Interactive Savings calculator
www.consumerfed.org/calculator.html
at an overhead display. Student enters her/his age, amount saved per week, and
annual rate of return. Ask the class to predict the result before you press enter.
(Generally their estimate will be very low.) This black-box calculator will produce the
amount saved in 20 years, or at age 65. Change the rate of return, get a new
estimate, and try again. The class should be impressed.
2. Students work in pairs (2 periods). Each pair needs a copy of both worksheets and
a computer with spreadsheet software. Internet access on one classroom computer
is useful for demonstration. Access for each pair is desirable for extensions, but not
required.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
3. Whole class summary and discussion. As time permits, explain the impact of
inflation: $1,000,000 in 45 years may not be worth what it is today. Use the Inflation
Calculator at www.NewsEngin.com to demonstrate this.
Classroom/ Information Management
After the teacher introduces and motivates the tasks, and distributes the work pages,
the students should proceed through the tasks on their own. The teacher will monitor
student behavior, assist pairs as needed, and emphasize time.
Assessment
After completing both worksheet activities, students will write a short narrative to
summarize their findings. They will include a table or graph or both. They will share
and compare their findings with another group. Selected examples will be discussed
with the whole class.
Tools and Resources
Some suggested links and extensions are
• Interactive Savings calculator
www.consumerfed.org/calculator.html
• AITLC Student Guide to Economics and Business
tlc.ai.org
• Buying My First Car
score.kings.k12.ca.us/lessons/firstcar.htm
• Free Tools-- Inflation Calculator
www.NewsEngin.com
Worksheets
Activity worksheets continue on the next page.
Worksheet 1:
Letting Money Grow for You
Worksheet 2: Interest, The Cost of MoneyWorksheet 1: Letting Money Grow
for You
Basic principles of compound interest1 :
Small amounts grow to very large amounts over time.
The sooner you start saving, the better.
Small differences in interest rates will make a very large difference over time.
So, the variables are
the amount saved each month or year,
how long you save, and
the interest rate.
==================================================================
1. With your partner, estimate:
a. If you save or invest money and earn interest, how much do you think you’d have
to save every year to have $100,000 in 20 years? __________________
1
Cruz, Humberto, “Math we Just Don’t Get”, The Beacon Journal. 11-22-99, D3.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
b. Divide your answer above by 50. ________________
This is the goal to save every week.
c. Brainstorm 3 possible ways you can reduce your spending. For ex, if you buy
soft drinks, 1 less coke each day can save about $4 a week or $200 a year.
___________________________
___________________________
___________________________
2. Create a new spreadsheet as shown below. Enter the formulas shown in A3 and
B3. Then extend these columns (Calculate-->Fill down) to cover 20 years. To
simplify the size of the spreadsheet, we assume that savings and interest on your
bank account are deposited only once each year. In reality, interest may be added
(“compounded”) daily! Format Column B as currency, 2 places, commas.
3. Study the 2 formulas in the spreadsheet.
Describe the function of A3 in a sentence:
____________________________________________________
Explain (1+ $C$4) _____________________________________
Now describe B3 in a sentence: _____________________________________
4. Experiment with the spreadsheet. Enter your estimate from 1a into C2. Does this
choice of yearly savings and interest rate give you more or less than $100,000 in
year 20?
Continue to play “what-if?”. You can change the entries for yearly savings amount;
you can change the interest rate. List 4 combinations of savings and interest rates
that produce $100,000 in 20 years.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
4. Make a spreadsheet chart for each different interest rate. (Just chart column B)
Create a line graph. Describe the shape of the chart for each rate. What is the
same? What is different as the rate increases?
5. For someone starting work and a savings plan today, it’s quite reasonable to set a
much higher goal.
• Modify the spreadsheet to extend for 45 years.
• Also consider the realistic possibility that you will increase your annual savings
each year, as you earn more. Change the formula in B3 to increase your annual
savings either by a constant dollar amount, or by a small constant percent .
6. After you explore several combinations of increasing annual savings, and changing
interest rates, write a 1-page summary report. Please be sure to discuss what
happened in relation to your specific changes in the spreadsheet. Include at least
one graph.