Copyright © 2005 Pearson Education, Inc. Slide 4-1.

Copyright © 2005 Pearson Education, Inc.

Chapter 4


Definitions

The principal in financial formulas is thebalance upon which interest is paid.

Simple interest is interest paid only on the original principal, an not on any interest addedat later dates.

Compound interest is interest paid on both theoriginal principal and on all interest that hasbeen added to the original principal.

4-A


Compound Interest

4-A

Principal + 6% Interest

(compounded quarterly for one year)

$1004

4

06. 1

Principal + 6% Interest (compounded quarterly for 10 years)

$100 years) 10by periods gcompoundinquarterly 4(multiply 01 4

4

06. 1


Compound Interest Formulafor Interest Paid n Times per Year

4-A

)(APR + 1 =

nY

nPA

A = accumulated balance after Y years P = starting principalAPR = annual percentage rate (as a decimal) n = number of compounding periods per year Y = number of years (may be a fraction)


APR vs. APY

4-A

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 increasestarting principal


Euler’s Constant e

4-A

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.

n = number of compoundings A = accumulation 1 = year 2.0 4 = quarters 2.44140625 12 = months 2.6130352902236 365 = days 2.7145674820245 365•24 = hours 2.7181266906312 365•24•60 = minutes 2.7182792153963 365•24•60•60 = seconds 2.7182824725426 infinite number of compoundings e 2.71828182846

1) (1.0 + 11 =

n

nA

Leonhard Euler(1707-1783)


Compound Interest Formulafor Continuous Compounding

4-A

) ( = YPA APRe

P = regular payment (deposit) amount

A = accumulated balance after Y years

e = the special number called Euler’s constant orthe natural number and is an irrational numberapproximately equal to 2.71828

Y = number of years (may be a fraction)

APR = annual percentage rate (as a decimal)


Social Security and Savings Plans

4-B

“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.


Savings Plan Formula(Regular Payments / Annuity)

4-B

Y = number of years (may be a fraction)

( )

APR 1 + 1

= PMT APR

nY

nA

n

A = accumulated balance after Y years

PMT = regular payment (deposit) amount


n = number of payment periods per year


Total / Annual Return Formulas

4-B

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:

The annual return is the average annual percentage yield (APY) that would give the same overall growth.

1 )/1(

=return annual

Y

P

A

PPA ) ( =return total


Total Return Formula

4-B

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?

57.8% = 27,500

27,500) (43,400 =return total


Annual Return Formula

4-B

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?

5.2% = 1 (1/9)

27,50043,400 =return annual


Potential Retirement Sources

4-B

1. Pension2. Personal Savings3. Social Security


Types of Investments

4-B

1. Stocks2. Bonds3. Cash4. Mutual Funds


Investment Considerations

4-B

1. Liquidity2. Risk3. Return


Stock Market Trends

4-B


Mutual Fund Quotations

4-B


Loan Payment Formula(Installment Loans)

4-C

P = starting loan principal (amount borrowed)

)(APR + 1 1

APR =PMT

nY

n

nP

PMT = regular payment

Y = loan term in years

n = number of payment periods per year



Loan Amortization Example

4-C


The Relationship BetweenPrincipal and Interest for a Payment

4-C


Income Tax Preparation Flow Chart

4-D


Federal Surplus / Deficit and Overall Debt

4-E


Federal Government Outlays

4-E

Copyright © 2005 Pearson Education, Inc. Slide 4-1.

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