Business

http://zonalandeducation.com/mmts/functionInstitute/exponentialFunctions/compoundInterest.html

Compound Interest Calculator (Yearly Interest r Simplified Compound Interest) http://math.about.com/library/blcompoundinterest.htm

Math Expression’s Simplified Compound Interest formula http://www.mathexpression.com/compound-interest-formula.html

Video Training: http://www.mathexpression.com/calculate-compound-interest.html

Dan Lamay's Compound Interest https://www.youtube.com/watch?v=bQtcRSH1zDc&feature=youtu.be

Simplified Compound Interest Equation http://math2.org/math/general/interest.htm

If you want monthly compound Interest – the formula gets a little bit more complex to accomidate the # of times per year interest in compounded.

http://math2.org/math/general/interest.htm

The Compound Interest Equation

P = C (1 + r/n)^nt

P = future value

C = initial deposit

r = interest rate (expressed as a fraction: eg. 0.06)

n = # of times per year interest in compounded

t = number of years invested

Continuous Compound Interest

When interest is compounded continually (i.e. n -->), the compound interest equation

P = C e ^rt

Demonstration of Various Compounding

The following table shows the final principal (P), after t = 1 year, of an account initally with C = $10,000.00 at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.

n (# of payments per year) p (Name of payment type) p (final principal)

1 (yearly) $10,600.00

2 (semi-annually) $10,609.00

4 (quarterly) $10,613.64

12 (monthly) $10,618.00

52 (weekly) $10,618.31

365 (daily) $10,618.37

Situation: A person initially borrows an amount A and in return agrees to make n repayments per year, each of an amount P. While the person is repaying the loan, interest is accumulating at an annual percentage rate of r, and this interest is compounded n times a year (along with each payment). Therefore, the person must continue paying these installments of amount P until the original amount and any accumulated interest is repayed. This equation gives the amount B that the person still needs to repay after t years.

B = A (1 + r/n)^nt - P = [(1 + r/n)^nt - 1] / [(1 + r/n) - 1]

B = balance after t years

A = amount borrowed

n = number of payments per year

P = amount paid per payment

r = annual percentage rate (APR)

Depreciation

College-cram is a good site to find definitions for Business Math. Here is a link to their Depreciation Study Sheet. http://www.college-cram.com/study/businessmath/depreciation/depreciation-study-sheet

Residual Value - also can be stated as Salvage Value, what is the value of a fixed asset after it has fully depreciated, or at the end of its useful life. http://www.investopedia.com/terms/r/residual-value.asp

Useful Life - is an estimate of how long something can be expected to be useful to the business (not how long it will actually last) The IRS defines "useful life" for estimating the amount of time over which an asset can be depreciated. InvestOpedia has a great dictionary http://www.investopedia.com/terms/u/usefullife.asp

Book Value - the value of the asset. Each year after depreciation, it is theoretical value of an asset if it were to be sold. http://www.investopedia.com/terms/b/bookvalue.asp

Depreciation - http://www.scribd.com/doc/47730829/Depreciation is a systematic and rational process of distributing the cost of tangible assets over the life of assets. Depreciation is a process of allocation. Cost to be allocated = acquisition cost - salvage value Allocated over the estimated useful life of assets. Allocation method should be systematic and rational.

Depreciation methods and formulas based on time

Straight line method (simplest)

Declining balance method

Sum-of-the-years'-digits method

Depreciation based on use (activity)

Depreciation = (Cost - Residual value) / Useful life

Depreciation = Book value x Depreciation rate

Depreciation expense =

(Cost - Salvage value) x Fraction

Fraction for 1st year = n / (1+2+3+...+ n)

Fraction for 2nd year = (n-1) / (1+2+3+...+ n)

Straight Line Depreciation Method

[Straight line depreciation Example]

On April 1, 2011, Company A purchased an equipment at the cost of $140,000. This equipment is estimated to have 5 year useful life. At the end of the 5th year, the salvage value (residual value) will be $20,000. Company A recognizes depreciation to the nearest whole month. Calculate the depreciation expenses for 2011, 2012 and 2013 using straight line depreciation method.

· Depreciation for 2011= ($140,000 - $20,000) x 1/5 x 9/12 = $18,000 Note: 9/12 because purchased in April only got 9 months of use.

· Depreciation for 2012= ($140,000 - $20,000) x 1/5 x 12/12 = $24,000

· Depreciation for 2013= ($140,000 - $20,000) x 1/5 x 12/12 = $24,000

For your example we can do out the depreciation for the life of the asset

RISK

Expected risk premium on stock = beta X expected risk premium on market

r - rf = B(rm - rf)

where rm = Expected rate of return on market portfolio

rf = risk-free interest rate

Suppose you are asked what the value 'of the common stock' is...

Given a dividend of 2.10. you only need to know what the net rate of return is to calculate the value of the initial investment (the common stock, in this case.)

How you would calculate this net rate of return is a business question.

However, suppose that the rate of return were 9%, and a dividend were 1.05. then we could say: Stock price X rate of return = Dividend

Therefore, in this example, we would have to let P = the stock price (our unknown we want to find and substitute the above to resemble:

P X (.09) = 1.05 BECOMES P = 1.05 / .09 SO THAT P = 11.67 would mean that our initial stock price would have been 11.67.

Limits - Rate of Change

http://www.intmath.com/differentiation/differentiation-intro.php

I like the way these were explained - and links to definitional and more examples:

1. Limits and Differentiation http://www.intmath.com/differentiation/1-limits-and-differentiation.php

2. The Slope of a Tangent to a Curve (Numerical) http://www.intmath.com/differentiation/2-slope-tangent.php

3. The Derivative from First Principles http://www.intmath.com/differentiation/3-derivative-first-principles.php

4. Derivative as an Instantaneous Rate of Change http://www.intmath.com/differentiation/4-derivative-instantaneous-rate-change.php

Maximizing (profits)

Free Book: Safari Books on-Line

http://my.safaribooksonline.com/book/math-and-science/9789332512085/1dot-linear-programming-formulation/ch1sec8_xhtml

Lots of good examples from North Carolina State University's Math faculty

http://www.math.ncsu.edu/ma114/PDF/2.2.pdf from Lavon B. Page

Profit = Revenue (or income) - Cost (or expenses) P=R-C or P = I - E

Total Profit = Total Revenue - Total Cost P = TR - TC

usually you will have limits included, like time, factory space, people, etc.

Maximizing Profit http://www.youtube.com/watch?v=6tNKEa_MlWg

Economics point of view:

Profit Maximization http://www.youtube.com/watch?v=devjsF8shrU

the Economists Jody http://www.youtube.com/user/jodiecongirl?feature=watch

Linear point of view:

from SheLovesMath http://www.shelovesmath.com/algebra/advanced-algebra/linear-programming/

Multiple Products and graph http://www.youtube.com/watch?v=3mnd_h-TM08

Using Excel

Understand Linear http://www.youtube.com/watch?v=S-W_eNsRiZ0

http://www.youtube.com/watch?v=Arv6t3uO73A

Business - Research & Analysis

Manufacturing

A casting when first poured is 17.875 cm long. The casting shrinks 0.188 cm as it cools. What is the percent shrinkage?

Change / Original = % /100

Change / Original * 100 = %

EX. a 5 gallon container of gas that lost a gallon of gas what percentage of gas did it loos?

1/5 = 5/100 or 1/5 * 100 = % --> 1(100)/5 = 20%

Matrix & Inverse Matrix

She Loves Math has a nice summary of Matrix and Matrix Inverse Rules along with examples

http://www.shelovesmath.com/algebra/advanced-algebra/matrices-and-solving-systems-with-matrices

Khan Academy shows how to apply the Matrix Inverst Rules described in SheLovesMath

https://www.khanacademy.org/math/precalculus/precalc-matrices/finding-inverse-matrix-with-determinant/v/inverse-of-a-2x2-matrix

More Khan on Matrix (but not all)

https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-formula-for-2x2-inverse

Logistic Equation

Definition https://en.wikipedia.org/wiki/Logistic_function

Patrick Just Math demonstrates at 2 min in - using the Logistic Equation: https://www.youtube.com/watch?v=MIOj-W-jY-k

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