What is the Value of Your Money?

Author: Peter Lindstrom

Within the next ten years, you will possibly purchase a stereo, borrow money to attend college, purchase a car, invest money in a savings plan, buy a home, enter into a retirement plan, etc. In each of these transactions, various mathematical formulas are used to determine the size of your monthly payments, the amount of interest you earn on an investment, the amount of interest you pay when you barrow money, etc. The examples and exercises (You Try Its) will show you how to use some of these mathematical formulas. At the same time you will see how to avoid newspaper and television advertisements that "seem to offer great bargains" but are actually "frauds in disguise."

Note: The information below was created with the assistance of AI.

Level of Mathematics

This lesson is most appropriate for:

High school students, especially those in grades 10–12, taking Algebra II, Financial Math, or Consumer Mathematics.
Also suitable for college prep courses or introductory business math.
Strong fit for personal finance units that aim to integrate algebra and real-world decision-making.

The lesson requires basic algebra, geometric series familiarity, and calculator skills, but not calculus.

Application Areas

The document is highly practical and connects math to real-life financial literacy topics:

Banking and savings: Simple and compound interest.
Loans and debt: Car loans, student loans, and installment payments.
Consumer decision-making: Interpreting advertisements, comparing payment plans.
Personal investment strategies: Future value of annuities and savings.

These applications help students see how math directly impacts their financial decisions and empowers critical evaluation of financial offers.

Prerequisites

Students should be comfortable with:

Algebraic manipulation: Solving equations, isolating variables.
Exponential expressions: Especially using calculators for powers and roots.
Understanding percent rates: Translating between percentages and decimals.
Basic understanding of time and payment intervals (e.g., monthly, quarterly).
Reading financial contexts: Interpreting tables, payment plans, and amortization schedules.

The module assumes students can handle word problems and multi-step calculations.

Subject Matter

Key mathematical concepts covered in this module include:

1. Simple and Compound Interest

Formulas:
- Simple: $I = P r t$ , $A = P (1 + r t)$
- Compound: $A = P(1 + i)^n$
Comparing growth under different interest types.

2. Present and Future Value

Use of discounting to determine today's value of future payments.
Emphasis on the "time value of money" concept.

3. Annuities

Ordinary annuities: Fixed regular payments over time.
Formula:
- Future value: $\frac{(1 + i)^n - 1}{i}$
- Present value: $\frac{1 - (1 + i)^{-n}}{i}$

4. Geometric Series

Applied to regular deposits and withdrawals.
Series used to simplify calculations in compound scenarios.

5. Amortization and Loan Comparison

Car loan calculations.
Hidden costs in "no-down-payment" deals.
Finance charge comparison using present value.

6. Critical Thinking with Advertisements

Analyzing real ads to determine true cost.
Understanding legal and ethical implications (e.g., interest on sales tax).

Correlation to Mathematics Standards
Common Core High School Standards

Algebra

HSA-CED.A.1: Create equations in one variable to represent relationships.
HSA-REI.B.3: Solve linear equations and interpret solutions.
HSA-SSE.A.1: Interpret expressions in context.

Functions

HSF-IF.C.8b: Use properties of exponents to interpret exponential functions.
HSF-LE.A.3: Observe how quantities grow by equal factors over equal intervals.

Modeling

HSF-MF.A.1: Use mathematical models to represent and solve real-world financial problems.
HSM-MD.B.5: Use probability and financial reasoning in decision-making.