ROCHESTER INSTITUTE OF TECHNOLOGY

MEMORANDUM

Date: October 4, 2006

To: Sharon Warycka, Instructor, Technical Writing

From: Karyn Lewis, Student, Technical Writing

Subject: EXPANDED DEFINITION ASSIGNMENT

Audience and Use Profile

The following definition is written for students studying finance or business and adults learning to

manage their personal finances and obtain the greatest return from their investments. The

concepts of Interest, Future Value, Present Value, Annuity, Investment and Compounding are

vital to understanding and calculating Time Value of Money. They must have some knowledge

and experience with handling expenses and saving money, preferably owning a personal savings

or checking account themselves or looking into it.

TIME VALUE OF MONEY

Introduction

Time Value of Money is the core principle of finance that money available at the present time is

worth more than the same amount in the future, due to its potential earning capacity. This idea

holds that—provided money can earn interest—any amount of money is worth more the sooner it

is received.

The time value of money serves as the foundation for all other notions in finance. It impacts

business finances, consumer finances and government finances. Time value of money results

from the concept of interest. It can be used to compare investment alternatives and to solve

problems involving loans, mortgages, leases, savings, and annuities.

Example

Time value of money can be illustrated by the fact that a dollar received today is worth more than

a dollar received a year from now because today's dollar can be invested and earn interest as the

year elapses.

For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year

($100 multiplied by 1.05). Conversely, $100 received one year from now is only worth $95.24

today ($100 divided by 1.05), assuming a 5% interest rate.

These calculations demonstrate that time literally is money. The value of money now is not the

same as it will be in the future, and vice versa. So, it is important to know how to calculate the

time value of money in order to distinguish between the worth of investments that offer returns at

different times.

Operating Principle

The time value of money is based on the premise that people prefer to receive a certain amount of

money today, rather than the same amount in the future, all else equal. As a result, you demand

interest, paid either along the way or at the end. The interest compensates you for the time in

which the money could be put to productive use, the risk of default, and the risk of inflation.

Implicit in any consideration of time value of money are the rate of interest and the period of

compounding. Time Value of Money is determined by the mathematics of Compound Interest—

the difference between the value of a sum of money at one point in time and its value at another

point in time.

Three formulas are used to calculate the time value of money:

NOTE:

r = the required rate of return per time period

n = the number of time periods.

1. The present value formula is used to discount future money streams: that is, to convert

future amounts to their equivalent present day amounts. The following factors can convert

between present value and future value:

( Future Value / Present Value ) = ( 1+r )n

( Present Value / Future Value ) = 1 / ( 1+r )n

2. The future value formula is used to compound today's money into the equivalent amount at

some time in the future (i.e., to compound money in either a lump sum or streams of

payments). The following factors can be used to convert between future value and annuity

amount:

( Future Value / Annuity ) = [( 1+r )n – 1] / r

( Annuity / Future Value ) = r / [( 1+r )n - 1]

3. The present value of an annuity formula is used to discount a series of periodic payments of

equal amounts to the present day. Variations of this formula can find the future value of the

annuity, or solve for the annuity given the present value (for example, finding monthly

mortgage payments) or find the annuity given the future value (for example finding a

monthly payment needed to reach a retirement savings goal). The following factors can

convert between present value and annuity:

( Present Value / Annuity ) = ( 1+r )n - 1 / ( 1+r )n

( Annuity / Present Value ) = r ( 1+r )n / ( 1+r )n - 1

NOTE: Time Value of Money Tables, Financial Calculators, Spreadsheet Software, and Time Value of

Money Software can also be used to calculate the Time Value of Money.

Special Conditions

Time Value of Money also takes into account risk aversion—both default and inflation risk. 100

monetary units today is a sure thing and can be enjoyed now. In five years, however, that money

could be worthless or not returned to the investor. There is a residual time value of money,

beyond compensation for default and inflation risk, which represents simply the preference for

consumption now versus later. Inflation-indexed bonds notably carry no inflation risk. In the

United States for instance, Treasury Inflation-Protected Securities carry neither inflation nor

default risk, but pay interest.

References Kapoor, Dlabay, and Hughes. Personal Finance 8e. New York: McGraw-Hill/Irwin, 2007.

―Time Value of Money.‖ AOL Money & Finance. 2006. http://money.aol.com/basics/3canvas/_a/time-

value-of-money/20060609125509990001.