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

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Course Title: Contemporary Mathematics

Lecture Topic: Compound Interest and Annuities

Instructor: Roger Knobel

Institution: The University of Texas - Pan American

Backwards Design

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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

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OBJECTIVE

By the next class period, students will be able to:

  • Compute the future value of a fixed annuity earning compound interest.

The objectives will require that students be able to:

  • 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

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  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

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  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?
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