# 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:
* 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.
* Difficulties- Students may have difficulty:
* Being able to identify the type of finance problem.
* Distinguishing between present value, future value, and payments.
* 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:
* Determining future retirement account balances.
* 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:
* 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

* What is 5.3% of 720?
* 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?
* 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

* 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?
* 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?