### Chapter 4 (Part 2)

```Copyright © 2005 Pearson Education, Inc.
Slide 4-1
Chapter 4
4-A
Definitions



The principal in financial formulas is the
balance upon which interest is paid.
Simple interest is interest paid only on the
original principal, an not on any interest added
at later dates.
Compound interest is interest paid on both the
original principal and on all interest that has
been added to the original principal.
Slide 4-3
4-A
Compound Interest
Principal + 6% Interest
(compounded quarterly for one year)





.06 
\$100 1 

4 
4
Principal + 6% Interest (compounded quarterly for 10 years)





.06 
\$100 1 

4 
4  10
(multiply 4 quarterly compounding periods by 10 years)
Slide 4-4
Compound Interest Formula
for Interest Paid n Times per Year
4-A
(nY )

APR

A = P1+

n 





A
P
APR
n
Y
=
=
=
=
=
accumulated balance after Y years
starting principal
annual percentage rate (as a decimal)
number of compounding periods per year
number of years (may be a fraction)
Slide 4-5
4-A
APR vs. APY
APR = annual percentage rate (also known as nominal rate)
APY = annual percentage yield (also known as effective yield )
APR = APY when the number of compounding periods equals 1
APY > APR when the number of compounding periods is greater than 1
APY = relative increase = absolute increase
starting principal
Slide 4-6
4-A
Euler’s Constant e
Investing \$1 at a 100% APR for one year, the following table of
amounts — based on number of compounding periods — shows us
the evolution from discrete compounding to continuous compounding.





A = 11 + 1.0
n
(n  1)





n = number of compoundings
1 = year
4 = quarters
12 = months
365 = days
365•24 = hours
365•24•60 = minutes
365•24•60•60 = seconds
infinite number of compoundings
A = accumulation
2.0
2.44140625
2.6130352902236
2.7145674820245
2.7181266906312
2.7182792153963
2.7182824725426
e  2.71828182846
Leonhard Euler
(1707-1783)
Slide 4-7
Compound Interest Formula
for Continuous Compounding
4-A
A = P  e (APR  Y )
A = accumulated balance after Y years
P = regular payment (deposit) amount
APR = annual percentage rate (as a decimal)
Y = number of years (may be a fraction)
e = the special number called Euler’s constant or
the natural number and is an irrational number
approximately equal to 2.71828
Slide 4-8
4-B
Social Security and Savings Plans
“Social Security can furnish only a base upon which
each one of our citizens may build his individual
security through his own individual efforts.”
President Franklin D. Roosevelt
The Franklin Delano Roosevelt Memorial
in Washington D.C.
Slide 4-9
Savings Plan Formula
(Regular Payments / Annuity)
A = PMT 
A



APR 

1
+


n 






( nY )
4-B

 1

APR 

n 
= accumulated balance after Y years
PMT = regular payment (deposit) amount
APR = annual percentage rate (as a decimal)
n
= number of payment periods per year
Y = number of years (may be a fraction)
Slide 4-10
4-B
Total / Annual Return Formulas
Consider an investment that grows from an original
principal P to a later accumulated balance A :
The total return is the relative change in the
investment value:

total return = ( A P)
P
The annual return is the average annual percentage yield
(APY) that would give the same overall growth.





A 
annual return = 
P
(1/ Y )
1
Slide 4-11
4-B
Total Return Formula
Example:
Suppose that you decided to invest in some real estate
property in the year 2004. The amount of your original
investment is \$27,500. In the year 2013 you decide to sell
and receive \$43,400 for the property.
What is your total return percentage and annual return
percentage?
total return = (43,400  27,500) = 57.8%
27,500
Slide 4-12
4-B
Annual Return Formula
Example:
Suppose that you decide to invest in some real estate property
in the year 2004. The amount of your original investment is
\$27,500. In the year 2013 you decide to sell and receive
\$43,400 for the property.
What is your total return percentage and annual return
percentage?






annual return = 43,400
27,500
(1/9)






 1 = 5.2%
Slide 4-13
4-B
Potential Retirement Sources
1. Pension
2. Personal Savings
3. Social Security
Slide 4-14
4-B
Types of Investments
1. Stocks
2. Bonds
3. Cash
4. Mutual Funds
Slide 4-15
4-B
Investment Considerations
1. Liquidity
2. Risk
3. Return
Slide 4-16
4-B
Stock Market Trends
Slide 4-17
4-B
Mutual Fund Quotations
Slide 4-18
Loan Payment Formula
(Installment Loans)
4-C





APR 
P


n

PMT =
(nY )

APR 
1  1 +



n


PMT = regular payment
P = starting loan principal (amount borrowed)
APR = annual percentage rate (as a decimal)
n = number of payment periods per year
Y = loan term in years
Slide 4-19
4-C
Loan Amortization Example
Slide 4-20
4-C
The Relationship Between
Principal and Interest for a Payment
Slide 4-21
4-D
Income Tax Preparation Flow Chart