Evaluate financial expression using PEMDAS

by Andrea
(Otis, CO., U.S.)

using PEMDAS to evaluate financial arithmetic

How do I simplify the financial expression shown below to get this answer: 0.822?

500(1/(1+0.04)⁵)

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Jan 24, 2013

simplify expression
by: Staff

Answer

Part I

The arithmetic expression 500(1/(1+0.04)⁵) is a

calculation of the present value of a future cash payment of $500.

(The problem statement does not say what the monetary unit is.

I’m arbitrarily using the monetary unit of dollars.)

The general formula is:


                  FV           
          PV = --------  
               (1 + i)^t 


FV = future value = $500

PV = present value = the result of the calculation

i = interest rate for one time period = .04 
(The interest rate is 4%.  4% ÷ 100 = 0.04)

t = the number of time periods = 5
(5 time periods could represent 5 years, 5 months, 
or some other time period.  The problem statement 
does not say.)

A summary of the calculation for your problem is:


                  FV           
          PV = --------  
               (1 + i)^t 

                       1           
          PV = FV * -------  
                    (1 + i)^t 

                         1           
          PV = 500 * ----------  
                     (1 + .04)⁵ 

              1           
          ---------- =  0.8219271067594   
          (1 + .04)⁵ 
                         this is the 0.822  
                         you asked about in  
                         the problem statement 

          PV = 500 * 0.8219271067594  

          PV = 410.9635533797

-------------------------------------

Jan 24, 2013

simplify expression
by: Staff

-------------------------------------

Part II

How to calculate a value for the expression (1/(1+0.04)⁵)

Make sure you read how to download free formula calculators (at the end of this post).

(1/(1 + 0.04)⁵) = ?

To simplify this expression:

Use the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction

Step 1: evaluate PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

(1 / (1 + 0.04)⁵)

There is one parentheses to evaluate: (1 + 0.04)

(1 + 0.04)

= 1 + 0.04

= 1.04

After evaluating the expression inside the parentheses, the expression looks like this:

1 / (1.04)⁵

Step 2: evaluate EXPONENTS

PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

1 / (1.04)⁵

There is one exponent to evaluate.

(1.04)⁵

= (1.04) * (1.04) * (1.04) * (1.04) * (1.04)

= 1.2166529024

After evaluating the expression inside the parentheses, the expression looks like this:

1 / 1.2166529024

Step 3: MULTIPLICATION

PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

1 / 1.2166529024

There is no multiplication which needs to be completed

Step 4: DIVISION

PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

1 / 1.2166529024

There is one place where division must be completed: 1 ÷ 1.2166529024

1 / 1.2166529024

= 0.8219271067594

Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

The is no addition or subtraction which needs to be completed.

The final answer is: 0.8219271067594 (or 0.822, rounded to the nearest one-thousandths)

-------------------------------------

Jan 24, 2013

simplify expression
by: Staff

-------------------------------------

Part III

Verify that the answer really is “0.822” using A "Formula" Calculator.

The correct answer is based upon PEMDAS . . . PAMDAS applied mechanically.

A Formula Calculator (Smart Calculator) automatically takes PEMDAS order into account.

The person using the calculator does not need to be concerned about which numbers to evaluate 1st, 2nd, 3rd, etc.

Type the entire expression into the “formula” calculator, just as it appears: 1 / (1 + 0.04)^5
Don’t change anything.

You can download free formula calculators here:

Free Calculators

Download or Use "SMART" Calculators on-line for Free

http://calcute.com/

http://www.fox-toolkit.org/download.html

http://www.google.com/search?hl=en&q=2%2B2%3D&btnG=Search

http://www.alemoi.com/math/

Thanks for writing.

Staff
www.solving-math-problems.com

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Evaluate financial expression using PEMDAS

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