Compound Interest

8-1

Compound Compound

8

Interest Interest

Compound Chapter 8

Compound Compound

8

Interest Interest

8-2 To better understand how Compound Interest is calculated, let’s reiew how we calculate !imple Interest" The &ormula on which we base our calculation is'

#ormula #ormula

I $ %rt

Here we hae an amount, the %rincipal %rincipal,, which is multiplied by the Interest Rate and Rate and the Time the Time oer  oer which the Interest is earned" (s we will now see, Compound Interest uses Interest  uses the S  the S um um of P  of P  & I  & I as a base on which to calculate

new  Interest !

Compound Compound

8

Compound Interest

8-3

- Future Value

Interest Interest

'the interest interest on  on the principal

 plus the

interest o& prior  periods  periods

e.g. %rincipal ) prior period interest $ *++ +  $1000.00

$100.00

Interest &or the next  period  period is calculated on *+ *++ +  This method will continue over the life of the loan or investment. (See later example)

Compound Compound

8

Interest Interest

Compound Interest

8-4

- Future Value

'is the compounded amount  and is the #I.(/ amount o& the loan or inestment at the end of the last period!

Contrast this with… is the alue o& a loan or inestment TO"!

Compound Compound

8

Interest Interest

Compound Interest

8-5

- Future Value

'the calculation o& interest oer the li&e o& the loan or inestment Let’s assume that the interest rate is 10% pa.

Example:  %rincipal ) prior period interest $ *++ Interest is now calculated on *++ %rincipal0Compounded1 2 + $ *++

New P $110.00 to start next period  Graphically'

Compound Compound

8-6

Compound Interest

8

- Future Value

Interest Interest

Interest Interest

Interest Interest

Interest Interest

Interest Interest

(mount*+ *+ (mount 1!!.1

1!!1 110 1100

100

1000

110 100

11

11

11 0 100

11 0 100

Compoundin Compoundin Compoundin g Period g Period g Period

0

1

 "ime#ears

!

Compoundin g Period

&

Compound Compound

8

Interest Interest

Compound Interest

8-7

- Future Value

3hat happens i& the interest rate chan#es durin4 the li&e o& an inestment5

'(ample… '(ample…

Compound Compound

8

Interest Interest

Compound Interest

8-8

- Future Value

6ou hold an inestment &or a period o& 7 years Rates o& return &or each year are 7, 8, -+ and 9 respectiely I& you inested *+ at the be4innin4 o& the term, how much will you hae at the end o& the last year5

Compound Compound

8

Interest Interest

Compound Interest

8-9

- Future Value

  6ou hold an inestment &or a period o& 7 years Rates o& return &or each year are 7, 8, -+ and 9 respectiely I& you inested *+ at the be4innin4 o& the term, how much will you hae at the end o& the last year5

6ear +

6ear :

6ear ;

6ear 7

*+

*+7

*++:;:

*++88

*+ 2 0+ ) 71

*+7 2 0+ ) 81

*++:;: 2 0+ - +1 $ *++88

*++88 2 0+ )91

$ *+7

$ *++:;:

$ *+++8< '(lternatie '(lternatie

Compound Compound

8

Interest Interest

Compound Interest

8 - 10

- Future Value 6ou hold an inestment &or a period o& 7 years Rates o& return &or each year are 7, 8, -+ and 9 respectiely I& you inested *+ at the be4innin4 o& the term, how much will you hae at the end o& the last year5

+0+710+810910+91 $ *+++8<  Solvin#  Solvin# (lternatie (lternatie + -+  Solve for all  Solve for all $ears at at %% $ears Itis israre rare&or &or interest interest to to be be  It once! once! compounded onl$ onl$ once once per per $ear! $ear! compounded

8 - 11

Compound Compound

8

Interest Interest

Compoundin4 #re=uencies and %eriods )re*uen+, )re*uen+,

o. per per ear ear o.

Period Period

(nnually

+

+ year

 Semi annually

:

< months

>uarterly

7

; months

Monthly

+:

+ month

?aily

; $ +0++@1+: +uarterl$ $