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CA9GHRF2IUTmH96Jn0i2hfu5nKF5mzsjoNRJoCs5kEmpgHzlY4eQoPK5oPTZoPT2IZTSJ+E5oeNZ LlmDoTDKLRoqlc6IajTViyHmodgAoo2gYgrKYiXKHd0JIiman9i2n54Xo0r6MTNqkZt4Z9LF/1bV dV1GmVNAZWKEF6I+OqJACgT1+aDHuSd5tqRkGlhNSpFvZla4JE/1NFoAVqW/aIofmqU9CmRnQaJe aqL2OSTAV6Z+umdnWmZNdF+CtKbz9FJueqNwCo9OOKcRV6eH8aNo0WLbAUV/eqmK1p44Blb0lVlk VUu3xFJtOqVvmpVs2Kg7Sqc4Z6c/Gn6Y+qqVppmJtErL1anN9am0FKpsiqikqqimaqU6SnOqangO KVSweqykFpV7M07k1FXm9FWcmk6eKkvupKuHKqX4RKW/GqcmZmHI+q2IuZIhw1HMGl9dBa3Rmke3 Sq2gaqgtxavZWqptmVM5Bq72OqAA6S1vxMFR/NpR5TpHzupV0Mpc6kSoKRVPu4qtG5ZPH3ivDruP uvJNEtSv/PqvQeSs6EqwsGSwaoqw1ypmDxuymKmvEruvFEtZFtusGDuwtlqwuFqohASEIjuzEHsv JWuyJ/tDKRuwAlur0rqufnRmNDu0ERkyNwtOOauzFsuzGduyTKRmRBu1NaszR5u0yLWzAZuxbSa1 XIuSelO1VhtHWIuxb9a1Zju1gQO2YUtBKTsCcna2cOu1HKS2a4tBdBa3eCu3xhQIADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rate =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rate =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rate =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N =3D total accumulation
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rate =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
4
0.08
P =3D 1000,
 r =3D 0.08, K =3D 4,<= span style=3D'mso-spacerun:yes'>  i =3D         =3D 0.02, T =3D 20,
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N =3D total accumulation
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0006_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
4
0.08
P =3D 1000,
 r =3D 0.08, K =3D 4,<= span style=3D'mso-spacerun:yes'>  i =3D         =3D 0.02, T =3D 20,
N =3D (20 years)*(4 times per yea= rs) =3D 80
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N =3D total accumulation
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0015_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
4 times a year.  How m= uch will be there after 20 years?
4
0.08
P =3D 1000,
 r =3D 0.08, K =3D 4,<= span style=3D'mso-spacerun:yes'>  i =3D         =3D 0.02, T =3D 20,
N =3D (20 years)*(4 times per yea= rs) =3D 80
Hence A =3D 1000(1 + 0.02 )80 » 4875.44 $
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0007_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0007_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZAAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABj ACAAgAAAAP///wJzRI6py+0Po2yg2ouz3rz7D2ZHSJbmaY7oyrah6sayC8/2Ddb4zlt6D7T9gsTW sIhMBZLM1bEJ3TyjVN+yitVMs9Atl+n9IsNiIrkMPKN56jWu7RZe4905HWy/j/N6M7+f9gfIJjj4 Vmgol+g30ej4CAlZAAA7 ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
8 times a year.  How mu= ch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
the number of increase the number of periods K= ?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
8 times a year.  How mu= ch will be there after 20 years?
8
0.08
P =3D 1000,
 r =3D 0.08, K =3D 8,  i =3D         =3D 0.01, T =3D 20,
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0011_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
8 times a year.  How mu= ch will be there after 20 years?
8
0.08
P =3D 1000,
 r =3D 0.08, K =3D 8,  i =3D         =3D 0.01, T =3D 20,
N =3D (20 years)*(8 times per years) =3D 160
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0014_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
8 times a year.  How mu= ch will be there after 20 years?
8
0.08
P =3D 1000,
 r =3D 0.08, K =3D 8,  i =3D         =3D 0.01, T =3D 20,
N =3D (20 years)*(8 times per years) =3D 160
Hence A =3D 1000(1 + 0.01 )160 » 4913.82 $
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0012_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0012_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZAAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABj ACAAgAAAAP///wJ2jI+py+0P4wIB2Iuz3rz7D4aaIZbmiZ5kyrauuL7y/Mb0jYd2zvfX7gvegMKi i2hMqirKZgrpjHKg0uqPac2OsNouhevNUsPKMdloPgvTah+7zXvDcfI5rW6X4fNHMH/t9+cWKBhH WEh3iHinuKgnARkpOUlZAAA7 ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
100 times a year.  How mu= ch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
100 times a year.  How mu= ch will be there after 20 years?
100
0.08
P =3D 1000,
 r =3D 0.08, K =3D 100, i =3D         =3D 0.0008<= span lang=3DEN-US style=3D'font-size:133%;text-shadow:auto;color:#FFCC00;mso-fa= reast-language: ZH-CN'>, T =3D 20,
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0016_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAj AAEAgAAAAP/MAAIFjI+puwUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
100 times a year.  How mu= ch will be there after 20 years?
100
0.08
P =3D 1000,
 r =3D 0.08, K =3D 100, i =3D         =3D 0.0008<= span lang=3DEN-US style=3D'font-size:133%;text-shadow:auto;color:#FFCC00;mso-fa= reast-language: ZH-CN'>, T =3D 20,
N =3D (20 years)*(100 times per years) =3D 2000
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0017_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAj AAEAgAAAAP/MAAIFjI+puwUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
100 times a year.  How mu= ch will be there after 20 years?
100
0.08
P =3D 1000,
 r =3D 0.08, K =3D 100, i =3D         =3D 0.0008<= span lang=3DEN-US style=3D'font-size:133%;text-shadow:auto;color:#FFCC00;mso-fa= reast-language: ZH-CN'>, T =3D 20,
N =3D (20 years)*(100 times per years) =3D 2000
Hence A =3D 1000(1 + 0.0008 )2000 »  4949.87 $
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0018_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAj AAEAgAAAAP/MAAIFjI+puwUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0018_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYwAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABj ACAAgAAAAP///wJ2jI+py+0P4wIB2Iuz3rz7D4aaIZbmiZ5kyrauuL7y/Mb0jYd2zvfX7gvegMKi i2hMqirKZgrpjHKg0uqPac2OsNouhevNUsPKMdloPgvTah+7zXvDcfI5rW6X4fNHMH/t9+cWKBhH WEh3iHinuKgnARkpOUlZAAA7 ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
1000 times a year.  How mu= ch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
1000 times a year.  How mu= ch will be there after 20 years?
1000
0.08
P =3D 1000,    = ; 
 r =3D 0.08, K =3D 1000, i =3D         =3D 0.00008= , T =3D 20,
N =3D (20 years)*(1000 times per years) =3D 20000
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0020_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
1000 times a year.  How mu= ch will be there after 20 years?
1000
0.08
P =3D 1000,    = ; 
 r =3D 0.08, K =3D 1000, i =3D         =3D 0.00008= , T =3D 20,
N =3D (20 years)*(1000 times per years) =3D 20000
Hence A =3D 1000(1 + 0.00008 )20000 »  4952.72 $
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0021_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAk AAEAgAAAAP/MAAIFjI+pywUAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0021_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZAAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABj ACAAgAAAAP///wJzRI6py+0Po2yg2ouz3rz7D2ZHSJbmaY7oyrah6sayC8/2Ddb4zlt6D7T9gsTW sIhMBZLM1bEJ3TyjVN+yitVMs9Atl+n9IsNiIrkMPKN56jWu7RZe4905HWy/j/N6M7+f9gfIJjj4 Vmgol+g30ej4CAlZAAA7 ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
10000 times a year.  How mu= ch will be there after 20 years?
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
10000 times a year.  How mu= ch will be there after 20 years?
Hence A =3D 1000(1 + 0.000008 )200000 »  4953.00 $
r =3D annual compound = rate,
T =3D number of years,=
K =3D number of period= s per year
Let P =3D principal, i= =3D r/K and N =3D T*K
then  A =3D P(1 + i )N = =3D total accumulation
What happen if we keep everything the same but
increase the number of periods K?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0025_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhaQAqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABn ACkAgAAAAP///wKNjI+py+0PYwS02ouz3rz7zxngSJbmSYnoyrag6sayC8/2/Qb4zmt1D8T9gsTY sIhEHZPM0bIJDemi1M+zigVcs9QtF+r9MsNiJLlMPKOB6jWv7RZO4905HWy/j/N6M7+f9gfIJjj4 Vmgol+i3WATXaPIISSI5mWPZU4nZobm50emZARp6IWF6ipqqmlAAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
K times a year.  How mu= ch will be there after 20 years?
10000 times a year        = ;            &n= bsp;           4953.00 $
What happen if we keep everything the same but
increase the number of periods K?
1000 times a year        = ;            &n= bsp;             4952.72 $
100 times a year        = ;            &n= bsp;            = ;   4949.87 $
4 times a year         = ;            &n= bsp;            = ;  4875.44 $
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
K times a year.  How mu= ch will be there after 20 years?
10000 times a year        = ;            &n= bsp;           4953.00 $
What happen if we keep everything the same but
increase the number of periods K?
1000 times a year        = ;            &n= bsp;             4952.72 $
100 times a year        = ;            &n= bsp;            = ;   4949.87 $
4 times a year         = ;            &n= bsp;            = ;  4875.44 $
µ
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0026_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAH ACgAgAAAAP8AAAIqBBKmqMb9VoJTtlNdxjfqvnkcBZbkaaGfOqbu+rbw3CL2fWu2nu3xoSgAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
K times a year.  How mu= ch will be there after 20 years?
10000 times a year        = ;            &n= bsp;           4953.00 $
What happen if we keep everything the same but
increase the number of periods K?
1000 times a year        = ;            &n= bsp;             4952.72 $
100 times a year        = ;            &n= bsp;            = ;   4949.87 $
4 times a year         = ;            &n= bsp;            = ;  4875.44 $
µ
?
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0027_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAH ACgAgAAAAP8AAAIqBBKmqMb9VoJTtlNdxjfqvnkcBZbkaaGfOqbu+rbw3CL2fWu2nu3xoSgAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0027_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAH ACgAgAAAAP/MAAIqhBOmqJfN4FvTNRDpzVbuioFc+JXeqaFdyq4uqcKt3CE2c+M3ldnmoigAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
K times a year.  How mu= ch will be there after 20 years?
10000 times a year        = ;            &n= bsp;           4953.00 $
What happen if we keep everything the same but
increase the number of periods K?
1000 times a year        = ;            &n= bsp;             4952.72 $
100 times a year        = ;            &n= bsp;            = ;   4949.87 $
4 times a year         = ;            &n= bsp;            = ;  4875.44 $
µ
4953.03 $
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0028_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAH ACgAgAAAAP8AAAIqBBKmqMb9VoJTtlNdxjfqvnkcBZbkaaGfOqbu+rbw3CL2fWu2nu3xoSgAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0028_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAH ACgAgAAAAP/MAAIqhBOmqJfN4FvTNRDpzVbuioFc+JXeqaFdyq4uqcKt3CE2c+M3ldnmoigAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0028_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhaAAqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQBo ACkAgAAAAP///wKPjI+py+0PowS02ouz3rz73xngSJbmWYnoyraj6sZyDM/2/Qb4zm91D9z9gkTZ sIhcHZNM0rIJDemiVNCziqVcs9UtN+r9NsPiJLlcPKOD6nWv7RZO4905HWy/j/N6M7+f9gfIJjj4 Vmgol+i3iATXePIIWSI5mWMJVInpobnJ0empARqKoSNxipqqunoAUAAAOw== ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
K times a year.  How mu= ch will be there after 20 years?
10000 times a year        = ;            &n= bsp;           4953.00 $
What happen if we keep everything the same but
increase the number of periods K?
1000 times a year        = ;            &n= bsp;             4952.72 $
100 times a year        = ;            &n= bsp;            = ;   4949.87 $
4 times a year         = ;            &n= bsp;            = ;  4875.44 $
µ
4953.03 $
Continuous Compound
Accumulation
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0029_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAH ACgAgAAAAP8AAAIqBBKmqMb9VoJTtlNdxjfqvnkcBZbkaaGfOqbu+rbw3CL2fWu2nu3xoSgAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0029_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAtAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAH ACgAgAAAAP/MAAIqhBOmqJfN4FvTNRDpzVbuioFc+JXeqaFdyq4uqcKt3CE2c+M3ldnmoigAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0029_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjQAqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL ACkAgQAAAP/MAP///wECAwLYhI+pu+IPo5y02otzZrwz4YXiSJYmAp5lqrbue7IwJ8/2DQvBjid1 Dwx2dDse8CdMKlNF4w2pjPZkzcBTihX+qjNo9quCcl1esHlUHsfO7HBITSq3576R2uqR0/d6BNf5 sSdIc1KFRziYiNICp9CnCPaoYIgImSiZYHhYZ3kphdm59Bk6CLpGyjeKSmdq0rp6FfUK26VKezaL dsuWK9K7eyoKHGk7jPWbZ/yFPKScxVzpLDwtnQQdWE2tla0ddM29KAu+LT5+VGxu8+2YPnWsAR8v P0/vAFAAADs= ------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Formula for Continuous Compund-Interest
     
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Formula for Continuous Compund-Interest
Let P =3D principal= 3;
      r =3D ann= ual interest rate (compound continuously)
       T =3D num= ber of years
     A =3D accumulat= ion
   
     
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Formula for Continuous Compund-Interest
Let P =3D principal= 3;
      r =3D ann= ual interest rate (compound continuously)
       T =3D num= ber of year
     A =3D accumulat= ion
    then       A = =3D P*er*T     where e <= /span>» 2.71828..
     
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
continuously.  How much will be th= ere after 20 years?
Formula for Continuous Compund-Interest
Let P =3D principal= 3;
      r =3D ann= ual interest rate (compound continuously)
       T =3D num= ber of year
     A =3D accumulat= ion
    then       A = =3D P*er*T     where e <= /span>» 2.71828..
     
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest
Continu= ous Compound Interest
Example:  We deposited= $1000 in an account with
annual compound interest rater =3D 8%, compounded
continuously.  How much will be th= ere after 20 years?
        = ;      A =3D 1000* e0.08*20
Formula for Continuous Compund-Interest
Let P =3D principal= 3;
      r =3D ann= ual interest rate (compound continuously)
       T =3D num= ber of year
     A =3D accumulat= ion
    then       A = =3D P*er*T     where e <= /span>» 2.71828..
     
------=_NextPart_01C82DF7.4CF16680 Content-Location: file:///C:/6E8AA2D4/4ContinuousCompoundInterest_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Continuous Compound Interest