A Lesson Plan for

the Mathematics of Finance

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, I, for t years on an amount of P dollars at a rate of interest r per year for t years is

I = Prt.

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

A = P(1 + rt).

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?

t A I

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

A = P(1 + r/m)

.

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?

Annually-1

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

S = R .

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

P = R .

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!!!