percentages_for compound_in interest.ppt

Perse 6 ghussa ka mam good morning Due to some emergency I will change the frog hop on a little tea pot and Others

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2. © T Madas
£10000areinvestedinabuildingsocietyaccount.
Theaccountpaysanannualinterestof8%.
Calculatetheamountinthisaccountin6yearstime,
ifnomoneyisfurtherpaidinorwithdrawn.
Thisproblemwouldbeeasyifbanks/buildingsocieties
paidSIMPLEINTEREST:
I.e. 8% on the original amount for every year
Then: 8% of £10000
6 x£800
£10000 +£4800
Is this what usually happens?
=£800
=£4800
=£14800

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End of YearInterest CalculationStart of YearYear
1080010000 x 1.08100001
1166410800 x 1.08108002
15868.7414693.28 x 1.0814693.286
14693.2813604.89 x 1.0813604.895
13604.8912597.12 x 1.0812597.124
12597.1211664 x 1.08116643
This is what usually happens

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Thisisknownasthecompound
interestcalculation,whenatthe
endofagivenperiod,sayayear,
the“capital”andinterestis
reinvestedinarepetitivefashion
foranumberofyears.

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Canyouspotaneasiercalculation?
£10000areinvestedinabuildingsocietyaccount.
Theaccountpaysanannualinterestof8%.
Calculatetheamountinthisaccountin6yearstime,
ifnomoneyisfurtherpaidinorwithdrawn.

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Canyouspotaneasiercalculation?
Original
amount
Interest increase as a % multiplier
years
£10000areinvestedinabuildingsocietyaccount.
Theaccountpaysanannualinterestof8%.
Calculatetheamountinthisaccountin6yearstime,
ifnomoneyisfurtherpaidinorwithdrawn.
10000x1.08( )x1.08( )x1.08( )x1.08( )x1.08( )x1.08=
10000x1.08x1.08x1.08x1.08x1.08x1.08=
10000x (1.08)
6

7. © T Madas
Canyouspotaneasiercalculation?
£10000areinvestedinabuildingsocietyaccount.
Theaccountpaysanannualinterestof8%.
Calculatetheamountinthisaccountin6yearstime,
ifnomoneyisfurtherpaidinorwithdrawn.
10000x1.08( )x1.08( )x1.08( )x1.08( )x1.08( )x1.08=
10000x1.08x1.08x1.08x1.08x1.08x1.08=
remember the order of operations
10000 x1.586874 15868.74
=
=
10000x (1.08)
6

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9. © T Madas
( )
7
£1000wereinvestedatacompoundinterestrateof
5%perannum.
Calculatethevalueofthisinvestmentin7years,15
yearsand25yearstime.
In 7years:1000x1.05=1407.10
( )
15
In 15years:1000x1.05=2078.93
( )
25
In 25years:1000x1.05=3386.35

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Howmuchmoredoes£1000investedat10%
compound interestfor10yearsgainthan
£1000investedat10%simpleinterest?
Simple interest:10% of 1000 is £100
10 years earning £100 per year
gains £1000
The investment doubles to £2000
Compound interest: ( )
10
1000x1.1=2593.74
an extra £593.74

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13. © T Madas
Howmanyyearswillittake£100todoublein
valuewheninvestedat:
1.5%simpleinterest
2.5%compoundinterest
Simple interest:5%of100is£5
Everyyear£5isearned
Fortheinvestmenttodouble
another£100mustbegained
100÷5=20years

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Compound interest:Inorderforthe£100todouble
theinvestmentmustbeworth
£200innnumberofyears
( )
n
100x1.05=200
This is an equation which requires logarithmsto solve
We are going to use trial and improvement
Howmanyyearswillittake£100todoublein
valuewheninvestedat:
1.5%simpleinterest
2.5%compoundinterest

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( )
10
100x1.05=162.89n=10
( )
15
100x1.05=207.89n=15
( )
14
100x1.05=197.99n=14
Is the correct answer 14or 15years?
Inorderforthe£100todouble
theinvestmentmustbeworth
£200innnumberofyears
( )
n
100x1.05=200
Howmanyyearswillittake£100todoublein
valuewheninvestedat:
1.5%simpleinterest
2.5%compoundinterest
Compound interest:

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