# ERIE COMMUNITY COLLEGE TITLE III Algebra Project

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ERIE COMMUNITY COLLEGE
TITLE III
Algebra Project
Interdisciplinary Course Materials

Course: MT006, MT007, MT013

Cpurse Outline Topic: Compound Interest

Title: How much will my student loans really cost?

Project Description: The student will compute Compound Interest using the familiar Simple Interest
Formula. The student will then apply the information to the Compound Interest formula and
compare the two answers. Students will then research the typical cost of student loan over a 2 year
period and an appropriate interest rate. They will then compute the interest paid over different
periods of time using both methods.

Things to Learn Before Starting the Project: How to use percents to solve problems (including simple
interest problems), order of operations and exponents.

Author: Colleen Quinn (Mathematics)

Semester Created: Spring 2009

Resources: answer sheet, words to use in an Internet search engine, www.bankrate.com, excel worksheet

Contents:       I        Project sheet

II       Example of how to compute Compound Interest using the Simple Interest Formula

III      Project Questions

V        Project Extensions

Erie Community College
Title III Grant
Name_________________________________________________________________

How much will my student loans really cost?
Student loans and the cost of college can add up quickly, but when you repay your loans to the federal
government, how much interest do you end up paying in addition to your loan?

We will explore this using the simple interest formula: i = prt.

Marjorie recently finished her Associate’s Degree from Erie Community College. In order to afford college, she
had to take out Student Loans. The total amount of her loan is \$6,374.00. She was able to finance the loan with a
federal Stafford Loan at 6.80%, which is compounded annually. Find the amount, A, if she plans on paying off her
loan after 5 years.

Solution: Compute the interest for the first year, using the simple interest formula. Add this interest to the
principal to find the amount at the end of the first year. Repeat this process for the second year, using the
principal + the added interest for the principal. Repeat until you find the final amount after 5 years.

How much interest must Marjorie pay back the federal government for her loan? ______________________

What we have just computed is called Compound Interest. Compound Interest is interest computed on the
principal and any accumulated interest.

Using the information above, compute the compound interest using the following formula:

In this formula, A is the final amount, p is the principal, r is the annual rate of interest, t is time in years, and n is
the number of compounding periods per year.

What did you get for A, using the formula? _________________________________________

Compare your answer to the answer you got using the simple interest formula. What was the difference? Explain.

Activity:

Determine the amount of student loans a student would need to receive in order to complete a Bachelor’s
Degree, include the loans taken out for an Associate’s Degree. Determine the interest rate for such loans by
visiting www.bankrate.com. Assume it will take 10 years to pay back the loans and the bank compounds interest
quarterly. How much interest will you pay back?

Erie Community College
Title III Grant
a.)   How much money does it cost to complete an Associate’s Degree at ECC? ______________
b.)   Where did you find this information? _______________________
c.)   How much money does it cost to complete a Bachelor’s Degree? __________________
d.)   Where did you find this information? Which institution did you use to acquire this information?

e.) What is the total cost of student loans needed?

f.) What interest rate did you find to finance the student loans, and which banking institution did you use?

g.) Compute the total interest paid using the simple interest formula.

h.) Compute the total interest paid using the compound interest formula.

Extensions:

1.) Students can compare the cost of receiving a Bachelor’s Degree at a private college (such as Canisius) vs. a
SUNY school.
2.) Students can compare different rates.
3.) Students can look at how college savings could benefit their children or future children using the Present
Value Formula:

An Example to accompany Extension #3:

Nicholas is currently in eighth grade and intends to attend a state college when he finishes high school.
Nicholas’s parents currently have some money invested in mutual funds, but would like to invest this money in
a more secure investment now to pay for college in 4 years. If they will need \$25,000, how much do
Nicholas’s parents have to invest now in a 48-month CD that has a rate of 4.59% compounded monthly?

4.) Students can then explore a college savings plan using current bank rates and time for their
children/future children.

Answer to in class activity: A = \$85,301.85 Total Interest Paid: \$78,927.85
Erie Community College
Title III Grant

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