# Compound Interest

## Full text

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8 - 1 8 - 1 Compound Compound Interest Interest Compound Compound Interest Interest

## C

### Chapter 8

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8 - 2 8 - 2 Compound Compound Interest Interest Compound Compound Interest Interest

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To better understand howTo better understand how Cis calculated, let’s reiew how we calculateis calculated, let’s reiew how we calculateCompound Iompound Interestnterest

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calculation is' calculation is'

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Here we hae an amount, the %rincipal%rincipal, , which which isis multiplied by the

multiplied by the Interest RateInterest Rate and the and the Time Time oer oer which the Interest is earned"

which the Interest is earned"

(s we will now see,

(s we will now see, Compound InterestCompound Interest uses uses the

the S  S um ofum of P  P  & & I I as a base on as a base on which to calculatewhich to calculate

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Interest  Interest !!

Compound Compound Interest Interest Compound Compound Interest Interest

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Graphically'

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100 11 0 11 1000 110 1!!1 1100 100 100 11 0

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(mount *+(mount *+ 110 InterestInterest InterestInterest 100 InterestInterest 1!!.1 Compoundin g Period Compoundin g Period Compoundin g Period Compoundin g Period InterestInterest 11

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'(lternatie'(lternatie   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

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It is rare &or interest to be compounded onl\$ once per \$ear!

It is rare &or interest to be compounded onl\$ once per \$ear! 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

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Compound Interest Compound

Interest

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8 - 14 Compound Interest Compound Interest

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I& you compounded

&or

### annually, semiannually, or =uarterly

, what are the alues &or n and i 5

### o.

B o& Compoundin4

#re=uencies per year 0m1

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8 - 15 Compound Interest Compound Interest

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If you compounded

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annually, semiannually, or =uarterly ' what are the alues &or n and i 5

<

<

<

+ : 7

### >uarterly

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/ o Compounding )re*uen+ies per

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### #ormula

!tee !mith deposited *+, in a sain4s account &or 7 years at a rate o& 8

compounded semiannually

3hat is !tee’s interest and compounded amount5

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8 - 18 Compound Interest Compound Interest

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### \$ *+,;<8@

%rincipal *+, ) Interest ;<8@ Compounded *+,;<8@ sin4 %D \$ *+ n \$ 8

\$ 7

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8 - 19 Compound Interest Compound Interest

### nterest5

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8 - 20 Compound Interest Compound Interest

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I& you compounded

&or

at

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annuall\$' semi annuall\$' or *uarterl\$ '

what are the &inal amounts that you would hae at the end o& the three 0;1 years 5

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8 - 21 Compound Interest Compound Interest

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(l Jones deposited *+, in a sain4s account &or @ years at + pa (l Jones deposited *+, in a sain4s account

&or @ years at + pa

3hat is (l’s

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alue5 3hat is (l’s

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alue5 3hat is (l’s

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ompounded

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alue5 3hat is (l’s

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ompounded

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%D \$ *+<+@+ - *+ !imple!imple CompoundCompound

(l Jones deposited *+, in a sain4s account &or @ years at +(l Jones deposited *+, in a sain4s account &or @ years at +

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Endin4 Lalance Endin4 Lalance Compoundin4 %eriod Compoundin4 %eriod

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Le4innin4 Lalance Le4innin4 Lalance .ominal Rate .ominal Rate

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(nnual !emiannual >uarterly ?aily

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8 - 24 Compound Interest Compound Interest

Calculate the

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at

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6ou inested *< at 7@ compounded *uarterl\$ (&ter : years, the rate chan4ed to @:

compounded monthl\$

3hat amount will you hae 7+: years a&ter the initial

inestment5

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6ou inested *< at 7@ compounded *uarterl\$ (&ter : years, the rate chan4ed to @:

compounded monthl\$

3hat amount will you hae 7+: years a&ter the

initial inestment5

### years

*< i  \$ 7@7 #D+ \$ %D: #D+ \$ <0+)7@718 \$ <0+9;<1 \$ <@<+@ #D: i \$ @:+: #D: \$ \$ <@<+@0++;8@1 \$ *7<+ <@<+@0+)@:+:1; n \$ 0:271 \$ 8 n \$ :@2+: \$ ;

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### %repare a time-line’ as part o& the solution

6ou borrowed *@ at  compounded monthl\$ Nn the &irst and second anniersaries o& the loan, you made payments o& *:@

3hat is the balance outstandin4

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 + year : years *@ i  \$ +: #D+ - *:@ \$ %D: #D+ \$ @0+)+:1+: \$ @0+::91 \$ @;<+7@ %D: \$ @;<+7@ K  :@ \$ :8<+7@ #D: i \$ +: #D: \$ \$ :8<+7@0+::91 \$ *;<8; :8<+7@ 0+)+:1+: n \$ +: n \$ +:

6ou borrowed *@ at  compounded monthl\$

Nn the &irst and second anniersaries o& the loan, you made payments o& *:@ 3hat is the balance outstandin4 immediatel\$ followin# the second pa\$ment,

.ew Lalance.ew Lalance

\$ *;<8; K :@ \$ *@<8;

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6ou eFpect to need *+,@ in ; years 6our banO o&&ers 7 interest compounded semiannuall\$

How much money must you put in the banO toda\$ 0%D1 to reach your 4oal in

; years5

### Calculatin4 P resent  alue

%repare the solution'0a1 al4ebraically, and 0b1 by &inancial calculator

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8 - 31 Compound Interest Compound Interest

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### #ormula

i \$ 7: \$ :

6ou eFpect to need *+,@ in ; years

6our banO o&&ers 7 interest compounded semiannuall\$ How much money must you put in the

banO toda\$ 0%D1 to reach your 4oal in ; years5

P  \$ *+@0+):1-< n \$ ; 2 : \$ <

### Calculatin4 P resent  alue

+: < +@ 889 +,;;+9< \$ *+@ 2 888 \$ *+,;;+9<

### 0a1

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8 - 32 Compound Interest Compound Interest

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### #ormula

3hat amount must you inest now at @ compounded dail\$ to accumulate to *< a&ter + year5

A \$ m \$

#D \$ i \$ n \$

### Calculatin4 P resent  alue

P  \$ *<0+)@;<@1-;<@ \$ *< 2 9@+: \$ *@,7 @ ;<@ < ;<@ + +++ 9@+: @,7 @ ;<@ @;<@ +2;<@ \$ ;<@ *<

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Two pa\$ments o& *:: each must be made + and 7 years  from now I& money can earn @ compounded monthl\$,

what sin4le payment ; years &rom now would be

e*uivalent to the two scheduled pa\$ments, ?raw a Time-line?raw a Time-line

### Step 1

#ind the #D o& the payment that is moed &rom 6ear + to 6ear ; #ind the #D o& the payment that

is moed &rom 6ear + to 6ear ;

### Step 2

#ind the %D o& the payment that is moed &rom 6ear 7 to 6ear ; #ind the %D o& the payment that

is moed &rom 6ear 7 to 6ear ;

### Step 3

%repare the solution'0a1 al4ebraically, and 0b1 by &inancial calculator

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8 - 34 Compound Interest Compound Interest

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Two pa\$ments o& *:: each must be made + and 7 years  from now I& money can earn @ compounded monthl\$,

what sin4le payment ; years &rom now

would be e*uivalent to the two scheduled pa\$ments, ?raw a Time-line?raw a Time-line

### Step 1

*:: *::

 + year : years ; years 7 years

i \$ @+: n \$ :2+: \$ :7

### Step 2

#ind the #D o&

the payment that is moed &rom 6ear + to

6ear ;

#ind the #D o& the payment that is moed &rom 6ear + to

6ear ; #D+ \$ ::0+)@+:1:7 \$ ::0++791 \$ :7;8 0a1 #D+ %D+ %D: #D:  ow

:7;8

### =uialent P ayments

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## References

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