1. Topic-
Compound Interest
2. Content-

P is the principal (the initial amount you borrow or deposit)

r is the annual rate of interest (percentage)

n is the number of years the amount is deposited or borrowed for.

A is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

A = P(1 + r)n

Frequent Compounding of Interest:

What if interest is paid more frequently?

Here are a few examples of the formula:

Annually = P × (1 + r) = (annual compounding)

Quarterly = P (1 + r/4)4 = (quarterly compounding)

Monthly = P (1 + r/12)12 = (monthly compounding)

When you borrow money from a bank, you pay interest. Interest is really a fee charged for borrowing the money, it is a percentage charged on the principle amount for a period of a year - usually.

If you want to know how much interest you will earn on your investment or if you want to know how much you will pay above the cost of the principal amount on a loan or mortgage, you will need to understand how compound interest works.

* Compound interest is paid on the original principal and on the accumulated past interest.
3. Goals: Aims/Outcomes-
1. Understand what compound interest is
2. Know what the formula is and how to apply it
4. Objectives-
1. Calculate Compound Interest
2. Learn the formula and how to use it
5. Materials and Aids-
Worksheets, Ace questions, White boards, Markers, etc.
6. Procedures/Methods-

A. Introduction-

1. Define Compoun Interest
2. Give Formula

B. Development-

1. Give 2 or 3 examples of compound interest using the formula
2. Give the students a problem
3. Have someone come up to the board and show what they did

C. Practice-

1. Q: If an amount of $5,000 is invested for two years and the interest rate is 10%, compounded yearly:
A: At the end of the first year the interest would be ($5,000 * 0.10) or $500

2. Q: Aiden invested $10,000 for five years at an interest rate of 7.5% compounded quarterly

A: P = $10,000
i = 0.075 / 4, or 0.01875
n = 4 * 5, or 20, conversion periods over the five years

Therefore, the amount, S, is:
S = $10,000(1 + 0.01875)^20
= $ 10,000 x 1.449948
= $14,499.48

So at the end of five years Aiden would earn $ 4,499.48 ($14,499.48 - $10,000) as interest.

D. Independent Practice-

1. Q: If you invest a principal of $1000 at 10% compound interest paid monthly, then after the first month, the interest payment will be:

A: interest (first month) = 10% of $1000 = $100

2. Q: Suppose Karen has $1000 that she invests in an account that pays 3.5% interest compounded quarterly. How much money does Karen have at the end of 5 years?

A: The $1000 is the amount being invested or P. The interest rate is 3.5% which must be changed into a decimal and becomes r = 0.035. The interest is compounded quarterly, or four times per years, which tells us that n = 4. The money will stay in the account for 5 years so t = 5. We have values for four of the variables. We can use this information to solve for A.

So after 5 years, the account is worth $1190.34. Because we are dealing with money in these problems, it makes sense to round to two decimal places. Notice that the formula gives us the total value of the account at the end of the five years. This is not just the interest amount, it is the total amount. Since there are many variables in the equations, there are several ways that problems can be presented.

E. Accommodations (Differentiated Instruction)-

1. Split the students into groups based on the multiple intelligence work sheet
2. Give each group a different compound interest problem (ACE)
3. Have students put their answer on white board and present to class

F. Checking for understanding-

1. Give one more problem to check understanding
2. Review for the quiz
3. Answer any questions students have

G. Closure-

1. Give the students a quiz
7. Evaluation-
1. See how well they did on the quiz based on the worksheets we did in class
8. Teacher Reflection-
1. write in the senior project journal about my experience
2. Ask students for feedback

This Lesson Plan is available at (www.teacherjet.com)