Simple & CompoundInterest

Simple Interest

-Interest paid only on an initial amount deposited or

the amount borrowed

-The amount is called the PRINCIPLE

Term

-The length of TIME in years over which the $$ is deposited

or borrowed

Often expressed as “PER ANNUM”

Calculating Formula

The amount of simple interest accumulated on an investment or loan is calculated using this

formula

I = Prt

I = the amount of interest earned or dueP = the Principle

r = the annual interest rate(expressed as a decimal)

t = the term of investment or loan

For an investment:

Calculate the total value at the end of the term

using this formula:

A = P + I

A=final value of the investmentP=PrincipleI=Amount of Interest

ExampleYou want to invest

$5000 in an account that offers simple

interest.How much would the investment be worth at the end of a 2yr

term at 3%?

First change the interest rate to a decimle

3% = .03

Principle = $5000Term = 2yrs

I = Prt

I = $5000 x .03 x 2ysI= $300

Now calculate the final valueA=P+I

A= $5000 + $300A=$5300

Converting Interest to a

decimal4.75% converted to a

decimal

=4.75 ÷ 100 = .0475

Use the same Principleand calculate at a rate of

3.75% for 4 yrs

I = $5000 x .0375 x 4 = $750

Calculate the final value

A = $5000 + $750 = $5750

Let’s Try Shall we?

Compound Interest

A type of interest that is calculated on the principle, plus any

interest PREVIOUSLY earned

Example

-If you invest $$ for two years, but earn interest annually…

-the second year of interest will be calculated on the initial principle PLUS the interest it

earned in the 1st year

Example

-$5000 @ 3% for 2 yrs calculated using COMPOUND

Interest

Year 1I = $5000 x .03 x 1yr = $150A = $5000 + $150 = $5150

Example

Year 2I = $5150 x .03 x 1 = $154.50

A = $5150 + $154.50 = $5304.50

Therefore - $5000 compounded “annually” over

2yrs @ 3% = a return of $304.50

Compounding Period

If the interest is compounded annually = once/yr

Investments can have different compounding

periods

Example

Interest can be calculated “SEMI-Annually”

Twice/year

Interest can be calculated “QUARTERLY”4 x per year

Example

Interest can be calculated “MONTHLY”Once/Month

Interest can be calculated “DAILY”

Calculation Formula

A = P(1+r ) n

A = Final ValueP = Principler = Interest Raten = Number of compound periodst = term of investment/loan

nt

Example

Calculate the interest earned on $1000 put in an account

that offers 4%/annum compounded annually for 2yrs

Example

A = P(1+r ) n

A = $1000 x (1 + 0.04 ) 1

nt

1x2

A = $1000 x (1.04)

2

A = $1081.60

Compare w/Simple Interest

I = $1000 x 4% x 2

I = $1000 x .04% x 2

I = $80A = $1000 + $80 =

$1080Compound Int. = $1081.60