Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendix 4A The Time Value of Money

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Appendix 4A

The Time Value of Money

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-2

The Time Value of Money

• Time Value of Money: as long as an opportunity exists to earn interest, the value of money is affected by the point in time when the money is received– A dollar received today is worth more than a dollar

received in the future

– The sooner you receive money from an investment, the better

– The sooner your money can begin earning interest, the faster it will grow


Interest: The Basic Return to Savers

• Interest: the “rent” paid by a borrower for use of the lender’s money

• Simple Interest– Interest is paid only on the initial deposit

• Compound Interest– Interest is paid on the initial deposit and any interest accumulated

from prior periods– Interest is earned on interest– More frequent compounding periods provide higher true rate

of interest– Compounding periods range from annually to continuously


Figure 4A.1 Financial Tables


Figure 4A.2 Calculator Keys


Calculating Time Value: Computers and Spreadsheets

• Built-in routines similar to financial calculators– Values for variables are entered in individual cells

on spreadsheet

– Cells are linked by equations programmed to calculate time values

– Changes in variable values automatically update time values

• Provides flexibility to investors


Future Value: An Extension of Compounding

• Future Value: the amount a current deposit will grow to over a period of time when it is placed in an account paying compound interest

• Future Value Example: How much will $1,000 deposited into an account earning 8% compounded annually be worth in two years?


Future Value: Using an Excel Spreadsheet


Future Value of an Annuity

• Annuity: a stream of equal cash flows that occur at equal intervals over time

• Ordinary Annuity: an annuity where cash flows occur at the end of each period

• Future Value of an Annuity Example: What is the future value of $1,000 deposited at the end of each year for 8 years in an account earning 6% compounded annually?


Future Value of an Annuity: Using an Excel Spreadsheet


Present Value: An Extension of Future Value

• Present Value: the value today of a sum to be received at some

future date

• Present Value Example: How much would need to be deposited today into an accounting earning 6% compounded annually to grow to $500 in 7 years?


Present Value: Using an Excel Spreadsheet


Present Value of a Mixed Stream of Returns

• Mixed Stream of Returns: series of returns that have no special pattern

• Present Value of an Annuity Example: What is the present value of the following stream of returns discounted at 9%?

Table 4A.4 Mixed and Annuity Return Streams


Table 4A.5 Mixed-Stream Present-Value Calculation


Present Value of a Mixed Stream of Returns: Using an Excel Spreadsheet


Present Value of an Annuity

• Annuity: a stream of equal cash flows that occur at equal intervals over time

• Present Value of an Annuity Example: What is the present value of $50 deposited at the end of each year for 5 years in an account earning 9% compounded annually?


Present Value of an Annuity: Using an Excel Spreadsheet

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Appendix 4A

Additional Chapter Art


Table 4A.1 Savings Account Balance Data (5% interest compounded annually)


Table 4A.2 Savings Account Balance Data (5% interest compounded semiannually)


Table 4A.3 True Rate of Interest for Various Compounding Frequencies (5% stated rate of interest)

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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendix 4A The Time Value of Money