A Lesson Plan for

by

Mike Callinan and Larry Shook

The following lesson plan is designed for students who have studied integer
exponents. The mathematics of finance tends to grab the interest of students
because it associates rather sterile numbers with something students are
interested in... money. In addition to the motivational factor, it is also
very practical topic. My suggestion for implementing the lesson would be
to have a short introduction in which vocabulary is discussed but as quickly
as possible have students work on applications. In the following lessons
only exercises using Excel are given. These can be complimented with more
traditional exercises. To begin with, we need to introduce some vocabulary.

**Interest-**The fee paid for the use of someone else's money.

**Principal-**The amount of money borrowed or deposited.

**Simple interest-**Interest paid only on the amount deposited and not
on past interest.

**Future value-**The total amount of principal and interest in an account.
The account can be on either a loan or an amount that has been deposited.

**Compound interest-**Interest that is charged (or paid) on interest
as well as principal.

**Compound amount-**The amount of principal and interest in an account
that draws compound interest.

**Annuity-**An account in which a sequence of equal payments are made
at equal time intervals.

**Note: Some of the financial formulas are functions in Excel. Teachers
should decide if students are to be allowed to use these. The spreadsheets
and graphs below are active and have the formulas put in manually.
Lesson 1-Simple Interest**

The simple interest,

The future value or maturity value, **A**, of **P **dollars for
**t **years at a rate of interest of r per year is

After going over the details of making sure students enter t in years
(11 months = 11/12 years), have the students create the following Excel
document.

Suppose $2000(in each of the following exercises I have chosen $2000-one
summer worth of savings) is invested at 8% interest, how long would it take
to have $3500 in the account? This could lead to a discussion of how to
solve this problem algebraically?

Have students describe how fast the account is growing? How does this relate
to the graph?

**Lesson 2-Compound Interest**

If **P **dollars are deposited for **m** compounding periods per year
for **n** years at a rate of interest **r** per period, the compound
amount **A** is

.

In the following Excel exercise, have students examine the effects of changing
the compounding periods each year for the following problem.

Suppose the $2000 is invested at a rate of 8% for 10 years, what are the
compound amounts for the following compounding periods?

Semiannually-2

Quarterly-4

Monthly-12

Daily-365

Hourly-8760

Minute-525,600

Every second-31,536,000

Why is the graph not linear? The above graph is for the first two columns
on the worksheet.

**Note: **An additional exercise to accompany the following would be
to have students evaluate the following sequence (1 + 1/n) as n becomes large
using Excel.

**Lesson 3-Future Value of an Annuity**

The future value **S** of an ordinary annuity of **n** payments of
**R** dollars each at the end of consecutive interest periods with interest
compounded at a rate of** i**=r/m per period is

There are alternate ways of working problems like the following without
using the above formula. Excel is a very versatile medium for students to
explore and find alternate methods for solutions.

Suppose at the age of 18 a student begins putting away $2000 per year for
10, 20, 30, or 40 years, how much money will be in the account at the end
of each of the given years? In order to make changes in our assumptions
about the interest rate, the following Excel worksheet makes use of the
$ sign function.

**Lesson 4-Present Value**

The present value P of an annuity of n payments of R dollars each at the
end of consecutive interest periods with interest compounded at an interest
rate i=r/m per period is

A car costs $15,000. After a down payment of $1000, the balance will
be paid off in 48 monthly payments with interest of 12% per year on the
unpaid balance. Find the amount of each payment. Prepare an amortization
schedule for the loan.

Students will be surprised as they calculate the total amount of interest
paid on the loan.

This brings us to financing a home.

**Lesson 5-The Big Investment**

One of the biggest investments most people will ever make is buying a home.
The following exercise is designed for students to experiment around with
the length of the loan and interest rates.

After a down payment, a family can finance $100,000 for a home. Interest
rates vary slightly from bank to bank. Is this a big deal?

In the Excel chart, the interest rate and total payments are variable.
Students should be allowed explore payments as these two quantities vary.
As a final project, students might be asked to do an essay on financing
a house given several constraints such as maximum amount of monthly payments
or varying interest depending on the length of the loan. Students might
use graphs to support there conclusions.

There are numerous ways to assess students progress through this unit. Presentations,
essays, computer work, pencil and paper exercises and tests. These lessons
are designed for students to be active. Enjoy!!!