[PDF] Compound interest, number and natural logarithm

Math Formulas: Logarithm formulas

Logarithm formulas 1 y = log a x ()ay = x (a;x > 0;a 6= 1) 2 log a 1 = 0 3 log a a = 1 4 log a (mn) = log a m+log a n 5 log a m n = log a m log a n 6 log a m n

Worksheet: Logarithmic Function

Vanier College Sec V Mathematics Department of Mathematics 201-015-50 Worksheet: Logarithmic Function 1 Find the value of y (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log

Logarithms - Math - The University of Utah

Below is the graph of a logarithm of base a>1 Notice that the graph grows taller, but very slowly, as it moves to the right Below is the graph of a logarithm when the base is between 0 and 1 ***** *** 210 Graphing logarithms Recall that if you know the graph of a function, you can find the graph of

Logarithms and their Properties plus Practice

Definition of a logarithm: If and is a constant , then if and only if In the equation is referred to as the logarithm, is the base , and is the argument The notation is read “the logarithm (or log) base of ” The definition of a logarithm indicates that a logarithm is an exponent is the logarithmic form of

Properties of Exponents and Logarithms

ln x is called the natural logarithm and is used to represent log e x , where the irrational number e 2 : 71828 Therefore, ln x = y if and only if e y = x Most calculators can directly compute logs base 10 and the natural log orF any other base it is necessary to use the change of base formula: log b a = ln a ln b or log 10 a log 10 b

General Logarithms and Exponentials

General exponential functions For a > 0 and x any real number, we de ne ax = ex lna; a > 0: The function ax is called the exponential function with base a Note that ln(ax) = x lna is true for all real numbers x and all a > 0

Linear and Logarithmic Interpolation - CMU

Mar 24, 2004 · This, however, means that the logarithm of these values is on the appropriate linear scale Hence, if the axis in Fig 1 were in fact logarithmic, Eqn 1 would have to be replaced by logx2 ¡logx logx¡logx1 = 1 f ¡1 : (4) Solving this for x, we flnd the logarithmic interpolation formula x = xf 2 x 1¡f 1 (log) : (5) If for instance f = 1

Compound interest, number and natural logarithm

logarithm September 6, 2013 Compound interest, number e and natural logarithm Compound interest If you have money, you may decide to invest it to earn interest The

[PDF] comment mener une enquête policière pdf

[PDF] log10(2)

[PDF] rapport d'enquête questionnaire

[PDF] rapport d'enquête définition

[PDF] rapport d'enquête méthodologie

[PDF] rapport d'enquête de satisfaction

[PDF] exemple de rapport d'un questionnaire

[PDF] introduction rapport d'enquête

[PDF] rapport d'enquête de terrain

[PDF] rapport d'enquête policière

[PDF] compte rendu d enquête policière

[PDF] mps svt enquete policiere

[PDF] leucaena leucocephala description

[PDF] 35 règles pour sauver son couple pdf gratuit

[PDF] leucaena leucocephala fourrage

Compound interest, numbereand natural

logarithm

September 6, 2013

Compound interest, numbereand natural logarithm

Compound interest

If you have money, you may decide to invest it to earn

interest. The interest can be paid in many dierent ways.If the interest is paid more frequently than one per year and

the interest is not withdrawn, there is a benet to the inventor since the interest earns interest. This eect is called compounding. Banks oer accounts that dier both in interest rates and in compounding methods. Some oer interest compounded annually, some quarterly, and other daily. Some even oer continuous compounding.What is the dierence between a bank account advertising 8% compounded annually and the one oering 8% compounded quarterly?Assume we deposit $1000, nd the balanceBaftertyears (assume that the interest will not be withdrawn).

Compound interest, numbereand natural logarithm

Compound interest

If you have money, you may decide to invest it to earn

interest. The interest can be paid in many dierent ways.If the interest is paid more frequently than one per year and

the interest is not withdrawn, there is a benet to the inventor since the interest earns interest. This eect is called compounding. Banks oer accounts that dier both in interest rates and in compounding methods. Some oer interest compounded annually, some quarterly, and other daily. Some even oer continuous compounding.What is the dierence between a bank account advertising 8% compounded annually and the one oering 8% compounded quarterly?Assume we deposit $1000, nd the balanceBaftertyears (assume that the interest will not be withdrawn).

Compound interest, numbereand natural logarithm

Compound interest

If you have money, you may decide to invest it to earn

interest. The interest can be paid in many dierent ways.If the interest is paid more frequently than one per year and

the interest is not withdrawn, there is a benet to the inventor since the interest earns interest. This eect is called compounding. Banks oer accounts that dier both in interest rates and in compounding methods. Some oer interest compounded annually, some quarterly, and other daily. Some even oer continuous compounding.What is the dierence between a bank account advertising 8% compounded annually and the one oering 8% compounded quarterly?Assume we deposit $1000, nd the balanceBaftertyears (assume that the interest will not be withdrawn).

Compound interest, numbereand natural logarithm

Compound interest

If you have money, you may decide to invest it to earn

interest. The interest can be paid in many dierent ways.If the interest is paid more frequently than one per year and

the interest is not withdrawn, there is a benet to the inventor since the interest earns interest. This eect is called compounding. Banks oer accounts that dier both in interest rates and in compounding methods. Some oer interest compounded annually, some quarterly, and other daily. Some even oer continuous compounding.What is the dierence between a bank account advertising 8% compounded annually and the one oering 8% compounded quarterly?Assume we deposit $1000, nd the balanceBaftertyears (assume that the interest will not be withdrawn).

Compound interest, numbereand natural logarithm

Compound interest

After one year:

Annual compounding:B= 1000(1:08) = 1080,Quarterly compounding:B= 1000(1:02)4= 1082:43.The interest after one year is 8% for the annual compounding,

and 8:243% for the quarterly compounding.We call this interestEective annual rate. That means the eective annual rate tells you exactly how much interest the investment really pays.We call the 8% thenominal rate(nominal means "in name only").

Compound interest, numbereand natural logarithm

Compound interest

After one year:

Annual compounding:B= 1000(1:08) = 1080,Quarterly compounding:B= 1000(1:02)4= 1082:43.The interest after one year is 8% for the annual compounding,

and 8:243% for the quarterly compounding.We call this interestEective annual rate. That means the eective annual rate tells you exactly how much interest the investment really pays.We call the 8% thenominal rate(nominal means "in name only").

Compound interest, numbereand natural logarithm

Compound interest

After one year:

Annual compounding:B= 1000(1:08) = 1080,Quarterly compounding:B= 1000(1:02)4= 1082:43.The interest after one year is 8% for the annual compounding,

and 8:243% for the quarterly compounding.We call this interestEective annual rate. That means the eective annual rate tells you exactly how much interest the investment really pays.We call the 8% thenominal rate(nominal means "in name only").

Compound interest, numbereand natural logarithm

Compound interest

After one year:

Annual compounding:B= 1000(1:08) = 1080,Quarterly compounding:B= 1000(1:02)4= 1082:43.The interest after one year is 8% for the annual compounding,

and 8:243% for the quarterly compounding.We call this interestEective annual rate. That means the eective annual rate tells you exactly how much interest the investment really pays.We call the 8% thenominal rate(nominal means "in name only").

Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

Problem 1.Which is better: BankXpaying 8% annual rate compounded monthly, and BankYoering a 7:9% annual

rate compounded daily?For BankX:B= 1000(1:006667)12= 1083:00 after 1 year.For BankY:B= 1000(1:0002164)365= 1082:18 after 1 year.The eective annual rate of BankXis 8:3%, and of BankY

is 8:218%.Extra question:Write an expression for the balance in each bank aftertyears.Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

Problem 1.Which is better: BankXpaying 8% annual rate compounded monthly, and BankYoering a 7:9% annual

rate compounded daily?For BankX:B= 1000(1:006667)12= 1083:00 after 1 year.For BankY:B= 1000(1:0002164)365= 1082:18 after 1 year.The eective annual rate of BankXis 8:3%, and of BankY

is 8:218%.Extra question:Write an expression for the balance in each bank aftertyears.Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

Problem 1.Which is better: BankXpaying 8% annual rate compounded monthly, and BankYoering a 7:9% annual

rate compounded daily?For BankX:B= 1000(1:006667)12= 1083:00 after 1 year.For BankY:B= 1000(1:0002164)365= 1082:18 after 1 year.The eective annual rate of BankXis 8:3%, and of BankY

is 8:218%.Extra question:Write an expression for the balance in each bank aftertyears.Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

Problem 1.Which is better: BankXpaying 8% annual rate compounded monthly, and BankYoering a 7:9% annual

rate compounded daily?For BankX:B= 1000(1:006667)12= 1083:00 after 1 year.For BankY:B= 1000(1:0002164)365= 1082:18 after 1 year.The eective annual rate of BankXis 8:3%, and of BankY

is 8:218%.Extra question:Write an expression for the balance in each bank aftertyears.Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

Problem 1.Which is better: BankXpaying 8% annual rate compounded monthly, and BankYoering a 7:9% annual

rate compounded daily?For BankX:B= 1000(1:006667)12= 1083:00 after 1 year.For BankY:B= 1000(1:0002164)365= 1082:18 after 1 year.The eective annual rate of BankXis 8:3%, and of BankY

is 8:218%.Extra question:Write an expression for the balance in each bank aftertyears.Compound interest, numbereand natural logarithm

Using the Eective Annual Yield

If interest at an annual rate ofris compoundedntimes a year, i.e. r=ntimes of the current balanceis addedntimes a year, then, with an initial depositP, the balancetyears later is B=P 1 +rn nt:

Compound interest, numbereand natural logarithm

Increasing the Frequency of Compounding: Continuous CompoundingFind the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000
?Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingFind the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000
?Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingProblem 2.Find the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000

1:0725056:Compound interest, numbereand natural logarithm

Increasing the Frequency of Compounding: Continuous CompoundingFind the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000

1:0725056:

1 +0:0710;000

10;000

?Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingFind the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000

1:0725056:

1 +0:0710;000

10;000

1:0725079:The dierence is small (7.25056% and 7.25079%).

Compound interest, numbereand natural logarithm

Increasing the Frequency of Compounding: Continuous CompoundingFind the eective annual rate for a 7% annual rate compounded1000 times a year

10,000 times a year

1 +0:071000

1000

1:0725056:

1 +0:0710;000

10;000

1:0725079:The dierence is small (7.25056% and 7.25079%).

Compound interest, numbereand natural logarithm

Increasing the Frequency of Compounding: Continuous CompoundingQ: What happens if we compound more often still? A: The eective annual rate increases, but not increase indenitely. It tends to a nite value.

1 +0:07n

n1:0725082 whennis large.The values 1.0725082 is an upper bound that is approached as the frequency of compounding increase.When the eective annual rate is at this upper bound, we say that the interest is beingcompounded continuously.Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingQ: What happens if we compound more often still? A: The eective annual rate increases, but not increase indenitely. It tends to a nite value.

1 +0:07n

n1:0725082 whennis large.The values 1.0725082 is an upper bound that is approached as the frequency of compounding increase.When the eective annual rate is at this upper bound, we say that the interest is beingcompounded continuously.Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingQ: What happens if we compound more often still? A: The eective annual rate increases, but not increase indenitely. It tends to a nite value.

1 +0:07n

n1:0725082 whennis large.The values 1.0725082 is an upper bound that is approached as the frequency of compounding increase.When the eective annual rate is at this upper bound, we say that the interest is beingcompounded continuously.Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingQ: What happens if we compound more often still? A: The eective annual rate increases, but not increase indenitely. It tends to a nite value.

1 +0:07n

n1:0725082 whennis large.The values 1.0725082 is an upper bound that is approached as the frequency of compounding increase.When the eective annual rate is at this upper bound, we say that the interest is beingcompounded continuously.Compound interest, numbereand natural logarithm Increasing the Frequency of Compounding: Continuous CompoundingQ: What happens if we compound more often still? A: The eective annual rate increases, but not increase indenitely. It tends to a nite value.

1 +0:07n

n1:0725082 whennis large.The values 1.0725082 is an upper bound that is approached as the frequency of compounding increase.When the eective annual rate is at this upper bound, we say that the interest is beingcompounded continuously.Compound interest, numbereand natural logarithm NumbereIf interest of an annual rate 1 is compoundedntimes a year. Assume that we deposit of 1 million dollars, then the balance after 1 year is 1 +1n nIncrease the frequency of compounding, i.e. increasen, this balance tends to an upper bound2:71828.The upper bound is calledEuler constant, denoted bye.

1 +0:07n

n

1:0725082e0:07IfPis deposited at an annual rate 7% compounded

continuously, the balanceBaftertyear isB=P(e0:07)t.Compound interest, numbereand natural logarithm NumbereIf interest of an annual rate 1 is compoundedntimes a year. Assume that we deposit of 1 million dollars, then the balance after 1 year is 1 +1n nIncrease the frequency of compounding, i.e. increasen, this balance tends to an upper bound2:71828.The upper bound is calledEuler constant, denoted bye.

1 +0:07n

n

1:0725082e0:07IfPis deposited at an annual rate 7% compounded

continuously, the balanceBaftertyear isB=P(e0:07)t.Compound interest, numbereand natural logarithm NumbereIf interest of an annual rate 1 is compoundedntimes a year. Assume that we deposit of 1 million dollars, then the balance after 1 year is 1 +1n nIncrease the frequency of compounding, i.e. increasen, thisquotesdbs_dbs8.pdfusesText_14