Project: Money in the Bank

Money in the Bank

Introduction

You have been diligently saving money for the past few years and have accumulated $1000 in cash. The goal has been to save up enough money to buy a used car. You determine that it would be better to invest the money in a bank and collect interest until you are ready to make your big purchase. After speaking with a bank representative, you are given several different savings options. You will use your ability to work with exponential and logarithmic functions to determine the best savings plan.

Task

In this project you will play the part of a person seeking to invest money in a savings account or a certificate of deposit (CD). When considering different investment options there are several factors to consider: 1) interest rate 2) compounding periods (quarterly, monthly, or daily) and 3) length of contract (1 year, 2 year, etc.). Working together with your group, you will analyze data and make calculations to determine the best investment option for your money.

Instructions

Solve each problem in order and save your work along the way, as you will create a professional report at the conclusion of the project.

· First problem: Impact of Interest Rates

· Many banks try to attract customers by providing the best interest rates possible. In this exercise, you will analyze several different interest rates to determine the true impact of a higher rate. Recall that the formula for compound interest is , where P is principal, A is amount, r is the annual rate, m is the number of compounding periods, and t is the number of years. Using this formula determine the amount (A) of money for each different interest rate that you will have in the bank after one year if the interest is compounded monthly. Round to the nearest cent.

P (principal)	r (annual rate)	How often compounded	m (number of compounding periods)	t (number of years)	A (amount)
$1000	1%	Monthly	12	1 year
$1000	2%	Monthly	12	1 year
$1000	5%	Monthly	12	1 year
$1000	8%	Monthly	12	1 year

· Next, for each interest rate, determine how long (in years) it will take for your money to double. Round to the nearest year.

P (principal)	r (annual rate)	How often compounded	m (number of compounding periods)	t (number of years)	A (amount)
$1000	1%	Monthly	12		$2000
$1000	2%	Monthly	12		$2000
$1000	5%	Monthly	12		$2000
$1000	8%	Monthly	12		$2000

· Based on the data that you have gathered, write a statement about the effect of higher interest rates.

· Second Problem: Compounding Periods

· Along with changing interest rates, various banks use different compounding periods. Some of them compound monthly (12 times a year), others quarterly (4 times a year), and some compounded daily (365 times a year). In this exercise, you will analyze these three different types of compounding periods to determine their effect on the amount of interest. Recall that the formula for compound interest is where P is principal, A is amount, r is the annual rate, m is the number of compounding periods, and t is the number of years. Using this formula determine the amount (A) of money for each different compounding period.

P (principal)	r (annual rate)	How often compounded	m (number of compounding periods)	t (number of years)	A (amount)
$1000	5%	Annually	1	1 year
$1000	5%	Quarterly	4	1 year
$1000	5%	Monthly	12	1 year
$1000	5%	Daily	365	1 year

· Next, for each different number of compounding periods determine how long (in years) it will take for your money to double. Round to the nearest year.

P (principal)	r (annual rate)	How often compounded	m (number of compounding periods)	t (number of years)	A (amount)
$1000	5%	Annually	1		$2000
$1000	5%	Quarterly	4		$2000
$1000	5%	Monthly	12		$2000
$1000	5%	Daily	365		$2000

· Based on the data that you have gathered, write a statement about the effect of the number of compounding periods. Do you think that the interest rate or the compounding period has the greatest impact?

· Third Problem: Length of Contract

· If you obtain a Certificate of Deposit (CD) from a bank, one of the options is length of contract meaning the amount of time you guarantee that your money will stay in the account. Typically, longer lengths of contracts yield greater interest rates. However, you do not have access to your money for the specified number of years. Recall that the formula for compound interest is , where P is principal, A is amount, r is the annual rate, m is the number of compounding periods, and t is the number of years. Using this formula determine the amount (A) of money that you will have in the bank for each of the scenarios below.

P (principal)

r (annual rate)

How often compounded

m (number of compounding periods)

t (number of years)

A (amount)

$1000

Monthly

3 years

$1000

Monthly

5 years

· Based on your data, do you believe that it is worthwhile to have your money “locked up” for an additional two years in order to receive the higher interest rate? Explain your thinking.

· Fourth Problem: Purchasing a Car

· Now you have to decide how to save enough money to purchase a used car in three years. You have the $1000 that you saved up and you plan to continue working. According to your estimates, you can save an additional $60 per month to put towards the car purchase. After conducting some research at the banks, you have decided on two options (see below). You need to figure out which option will yield the most money after the three years.

Option #1-CD for 3 years

Interest rate of 3% compounded monthly.

No money can be added to the CD.

However you can save your money on the side.

Option #2-CD for 1 year

Interest rate of 2% compounded quarterly.

You can add money at the end of each year.

You will renew it each year for 3 years.

· Explain what you have learned about investing in terms of rates, compounding, and length of contract.

Collaboration

Get together with another group to compare your answers to each of the four problems. Discuss how you might combine your answers to make a more complete and convincing analysis of the situation.

Conclusions

Present your solution in a way that makes it easy for someone investing money to understand your results. Be sure to clearly explain your reasoning at each stage and conclude with recommendations about interest rates, compounding periods, and length of contract. You should look through bank advertisements to see what the current interest rates are for each type of CD and savings account. Explain how your results can transfer to these different situations.

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. Your project should correctly identify and justify mathematically: (1) impact of interest rates on amount of interest earned, (2) the differences between compounding periods, (3) the amount of interest earned for various lengths of contracts, and (4) recommendations for choosing a savings plan or CD. You will be evaluated based on the following:

Score

Content

Presentation/Communication

• The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution.

• The solution completely addresses all mathematical components presented in the task.

• The solution puts to use the underlying mathematical concepts upon which the task is designed and applies procedures accurately to correctly solve the problem and verify the results.

• Mathematically relevant observations and/or connections are made.

• There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.

• Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.

• There is precise and appropriate use of mathematical terminology and notation.

• Your project is professional looking with graphics and effective use of color.

• The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution.

• The solution addresses all of the mathematical components presented in the task.

• The student uses a strategy that includes mathematical procedures and some mathematical reasoning that leads to a solution of the problem.

• Most parts of the project are correct with only minor mathematical errors.

• There is a clear explanation.

• There is appropriate use of accurate mathematical representation.

• There is effective use of mathematical terminology and notation.

• Your project is neat with graphics and effective use of color.

• The solution is not complete indicating that parts of the problem are not understood.

• The solution addresses some, but not all of the mathematical components presented in the task.

• The student uses a strategy that is partially useful, and demonstrates some evidence of mathematical reasoning.

• Some parts of the project may be correct, but major errors are noted and the student could not completely carry out mathematical procedures.

• Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

• There is some use of appropriate mathematical representation.

• There is some use of mathematical terminology and notation appropriate of the problem.

• Your project contains low quality graphics and colors that do not add interest to the project.

• There is no solution, or the solution has no relationship to the task.

• No evidence of a strategy, procedure, or mathematical reasoning and/or uses a strategy that does not help solve the problem.

• The solution addresses none of the mathematical components presented in the task.

• There were so many errors in mathematical procedures that the problem could not be solved.

• There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem.

• There is no use or inappropriate use of mathematical representations (e.g. figures, diagrams, graphs, tables, etc.).

• There is no use, or mostly inappropriate use, of mathematical terminology and notation.

• Your project is missing graphics and uses little to no color.

Some rights reserved

Monterey Institute for Technology and Education 2011