UTPA STEM/CBI Courses/Business Math/Compound Interest and Annuities

Course Title: Contemporary Mathematics

Lecture Topic: Compound Interest and Annuities

Instructor: Roger Knobel

Institution: The University of Texas - Pan American

Backwards Design
Course Objectives


 * Primary Objectives- By the next class period students will be able to:
 * Compute the future value of a fixed annuity.


 * Sub Objectives- The objectives will require that students be able to:
 * 1) Identify the type of finance problem given a real world situation.
 * 2) Identify the payment amount, payment period, annual interest rate, and length (time) of the annuity.
 * 3) Convert an interest rate from percent form to decimal form.
 * 4) Compute the period interest rate and number of payments.
 * 5) Select the correct formula for computing the future value of a fixed annuity.
 * 6) Use a calculator to evaluate a finance formula.


 * Difficulties- Students may have difficulty:
 * 1) Being able to identify the type of finance problem.
 * 2) Distinguishing between present value, future value, and payments.
 * 3) Converting an annual interest rate in percent form to a periodic interest rate in decimal form.


 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * 1) Determining future retirement account balances.
 * 2) Determining periodic payments needed to achieve a savings or retirement goal.

Model of Knowledge


 * Concept Map
 * Simple Interest
 * Compound Interest
 * Understanding the fixed annuity formula.


 * Content Priorities
 * Enduring Understanding
 * Understand the power of compound interest and exponential growth.
 * Being aware that regular deposits over time into an interest earning account can lead to big things.
 * Important to Do and Know
 * Be able to compute the future value of a fixed annuity.
 * Worth Being Familiar with
 * The effect of different interest rates and periods in future investment values.

Assessment of Learning


 * Formative Assessment
 * Short in-class problem sets.
 * On-line quiz or homework.
 * Summative Assessment
 * Questions on the unit and final exams.

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Compute the future value of a fixed annuity earning compound interest.
 * Identify the type of finance problem given a real world situation.
 * Identify the payment amount, payment period, annual interest rate, and length (time) of the annuity.
 * Convert an interest rate from percent form to decimal form.
 * Compute the period interest rate and number of payments.
 * Select the correct formula for computing the future value of a fixed annuity.
 * Use a calculator to evaluate a finance formula.

THE CHALLENGE

You have won $500,000 in the lottery. You can take a lump sum now of $300,000, or $25,000 each year for 20 years. What would you pick; why?

GENERATE IDEAS


 * Collect, organize, compare, and contrast the different reasons for selecting each option.
 * Ask "What are reasons that someone would want the money now? What are reasons that someone would want the annual payments?"
 * Discuss "If your goal was to have as much money when you retire, what other information would you need to make a more informed decision?"

MULTIPLE PERSPECTIVES


 * Provide short video clips of lottery winners explaining what they did and why.
 * Use a spreadsheet to simulate deposits and compound interest.

RESEARCH & REVISE


 * Teacher led introduction of the fixed annuity formula.
 * Worksheets leading students through the use of the fixed annuity formula.

TEST YOUR METTLE


 * Small groups re-examining the challenge question, resulting in a poster with their explanation and conclusion.

GO PUBLIC


 * Homework problems giving students a variety of scenarios where the fixed annuity formula is used to compute a future value.

Pre-Lesson Quiz

 * 1) What is 5.3% of 720?
 * 2) You have $120 in a bank account earning 6.0% interest compounded monthly. How much would you have in your bank account after 1 month? After 2 months? After 3 months?
 * 3) Suppose you deposit $40 into an account earning 5% interest compounded daily. After three years, how many deposits have you made into the account?

Test Your Mettle Quiz

 * 1) Each year, you deposit $500 of your income tax return into an account earning 4% compounded annually. How much will you have in the account after 7 years?
 * 2) As part of a cash settlement, you have the choice of taking a one-time payment of $25,000 or annual payments of $2000 for 10 years. Assuming that you invest all of the money into an interest-bearing account, which option would allow you to accumulate the greater amount of money at the end of 10 years? Does your answer depend on the interest rate?