Pesonal finance 6th madura chapter 03 applying time value concepts

Personal Finance

SIXTH EDITION

Chapter 3
Applying Time Value
Concepts

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Chapter Objectives (1 of 2)
3.1 Describe the importance of the time value of money
3.2 Calculate the future value of a dollar amount that you save today
3.3 Calculate the present value of a dollar amount that will be received in the future
3.4 Calculate the future value of an annuity

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Chapter Objectives (2 of 2)
3.5 Calculate the present value of an annuity
3.6 Explain how time value can be used to estimate savings
3.7 Explain how time value fits within your financial plan

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The Importance of the Time Value of Money (1 of 2)

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The value of money is influenced by the time it is received

•

The value of a given amount of money is generally greater the earlier it is received

•

The earlier you start saving, the more quickly your money can earn interest and grow

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The Importance of the Time Value of Money (2 of 2)

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Can be applied to a single dollar amount—also called a lump sum

•

Can also be applied to an annuity

–

Annuity: a series of equal cash flow payments that are received or paid at equal intervals in
time

–

An example would be a monthly deposit of $50 into your savings account

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Future Value of a Single Dollar Amount (1 of 9)

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Compounding: the process of earning interest on interest

•

To determine the future value of an amount of money you deposit today, you must
know:

–

The amount of your deposit today

–

The interest rate to be earned on the deposit

–

The number of years the money will be invested

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Future Value of a Single Dollar Amount (2 of 9)

•

Future value interest factor (FVIF):
a factor multiplied by today’s savings to determine how the savings will accumulate
over time

•

Can be calculated using the future value table or a financial calculator

–

Future value table shows various interest rates (i) and time periods (n)

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Future Value of a Single Dollar Amount (3 of 9)

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Suppose you want to know how much money you will have in five years if you invest
$5,000 now and earn an annual return of 4 percent

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The present value of money (PV) is the amount invested, or $5,000

–

Find the interest rate of 4 percent and a time period of five years on the table

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Future Value of a Single Dollar Amount (4 of 9)

•

Using the information in the example and the table, we can determine that, in five
years, your money will be worth:

$5,000 x 1.217 = $6,085

•

The future value can also be determined using a financial calculator with the following
inputs; PV = -$5,000; N = 5; I/Y = 4; PMT = 0; CPT FV = $6,083.26*
*Note there is a slight rounding error between the two values.

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Future Value of a Single Dollar Amount (5 of 9)

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Impact of a longer period

–
–

As the number of years increases, the FVIF increases
What if you invested your $5,000 for 20 years instead of 5 years? Assuming the interest rate is
still 4%:
$5,000 x 2.191 = $10,955

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Future Value of a Single Dollar Amount (6 of 9)

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Impact of a higher interest rate

–
–

The higher the interest rate, the more your money will grow
What if you invested your $5,000 at an interest rate of 9% instead of 4%? Assuming a period of
20 years:
$5,000 x 5.604 = $28,020

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Future Value of a Single Dollar Amount (7 of 9)

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Future Value of a Single Dollar Amount (8 of 9)

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The power of compounding

–
–

An amount of savings can grow substantially due to compounding
Compounding can also expand your debt



Not only do you pay interest on your debt, you also pay interest on the interest on your debt

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Future Value of a Single Dollar Amount (9 of 9)

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Twisted logic about long-term debt

–

Some people believe that it is to their advantage to postpone payment of debt as long as
possible



–

More enjoyable to spend than to pay!

They fail to recognize how debt can accumulate over a long-term period

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Financial Planning Online (1 of 2)

•

Go to the banking section of About.com

•

This Web site provides information on how you can pay your bills online.

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Present Value of a Dollar Amount (1 of 5)

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Discounting: the process of obtaining present values

•

Present values tell you the amount you must invest today to accumulate a certain
amount at some future time

•

This amount is based on some interest rate you could earn over that period

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Present Value of a Dollar Amount (2 of 5)

•

To determine present values, you need to know:

–

The amount of money to be received in the future

–

The interest rate to be earned on the deposit

–

The number of years the money will be invested

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Present Value of a Dollar Amount (3 of 5)

•

Using the Present Value Table

–

Present value interest factor (PVIF):
a factor multiplied by a future value to determine the present value of that amount

–

•

Notice that PVIF is lower as the number of years increases and as the interest rate increases

Can also be calculated using a financial calculator

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Present Value of a Dollar Amount (4 of 5)

•

You would like to accumulate $50,000 in five years by making a single investment
today. You believe you can achieve a return from your investment of 7 percent
annually. What is the dollar amount that you need to invest today to achieve your goal?

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Present Value of a Dollar Amount (5 of 5)

•

Using the information in the example and the table we can determine that in order to
have $50,000 today:

$50,000 x 0.713 = $35,650

•

This can also be determined using a financial calculator with these inputs; FV =
$50,000; N = 5; I/Y = 7; PMT = 0; CPT PV = $35,649.30*

*Note there is a slight rounding error between the two methods.

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Future Value of an Annuity (1 of 4)

•

Annuity due: a series of equal cash flow payments that occur at the beginning of each
period

•

Ordinary annuity: a series of equal cash flows that occur at the end of each period

•

Timelines: diagrams that show payments received or paid over time

•

These values can also be calculated using a table or a financial calculator

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Future Value of an Annuity (2 of 4)

•

Future value interest factor for an annuity (FVIFA): a factor multiplied by the periodic
savings level (annuity) to determine how the savings will accumulate over time

–

i is the periodic interest rate

–

n is the number of payments in the annuity

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Future Value of an Annuity (3 of 4)

•

Suppose that you have won the lottery and will receive $150,000 at the end of every
year for the next 20 years. As soon as you receive the payments, you will invest them
at your bank at an interest rate of 7 percent annually. How much will be in your account
at the end of 20 years, assuming you do not make any withdrawals?

•

Note that this is an ordinary annuity

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Future Value of an Annuity (4 of 4)

•

Using our example and the table, we can determine that, at the end of twenty years,
you would have:

$150,000 x 40.995 = $6,149,250

•

This can also be determined using a financial calculator with these inputs; PMT = $150,000; N = 20; I/Y = 7; PV = 0; CPT FV = $6,149,323.85*
*Note there is a slight rounding error between these two methods.

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Financial Planning Online (2 of 2)

•

Go to the calculators in the personal finance section of Yahoo.com

•

This Web site provides several tools that, among other things, will help you estimate of
the future value of your savings

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