Equivalence & Interest

Introduction

Engineering economy is the analysis of the choice between alternatives using economic considerations.

An Engineer must :

1. Identify alternative uses for limited resources.
2. Obtain appropriate data.
3. Analyze data.
4. Determine the preferred alternative.

Eugene L. Grant the father of Engineering economy was the first to apply compound interest to comparisons of long term investments.

Equivalence & Interest (Building blocks of Engineering Economics)

Consider the following situation :

1.You give me $20 now.
2. I will repay you in 1 year.
3. How much do you want to be repaid?

Repayment amount = Original amount (called Principal) + Interest

Interest is rent for using money.

The lender is compensated for :

The borrower pays for the opportunity to use money he didn't have.

How much Interest do you want for the year?

Deposits in a bank account returns 4% (+ or -)

Your rate = Bank % return + % for risk = MARR
                               where MARR = Minimum Attractive Rate of Return

Rate of Return (ROR) = Repay amount - Amount Original   x 100%
                                                      Original amount

Lets say your risk is worth 2% & you can get 4% interest in a bank account.

Thus:  Repayment =  Original amount + Interest
                              =   $20 + 0.06(20)
                              =   $20 + $1.2   
                             =    $21.20

Hence $20 today in your pocket is equivalent to $21.20 in your pocket 1 year from now, at  
6% interest rate.

What amount 1 year ago is equivalent to $20 now at 6% interest rate?

       $20 / 1.06 = $18.87   

Thus :    1 year in past       6%        Now             6%               1 year in future 
                  $18.87              =           $20              =                        $21.20

Simple Interest:

Let us suppose the following situation occurs:

A sum of $1000 is borrowed. There is a 10% interest charge/year for 5 years. The original sum plus interest charge is to be paid back at the end of the loan.

                 Amount owed                                         Amount owed 
Year            Begin Year               10% Interest           End  Year
   1          1000(borrowed)                100                      1100
   2          1100                                 100                      1200
    3          1200                                 100                      1300
   4          1300                                 100                      1400
   5          1400                                100                      1500(Pay back)

  • Interest is only applied to the original sum borrowed.
  • No cash changed hands until the end.
  • Simple interest is only used by loan sharks in movies named Vinnie.
  • Use portions of year to calculate non-integer loan periods.

Standard Terms:

The following terminology is used in calculations:

     P = Present worth or Principal = Amount originally loaned or borrowed
     F = Final or future worth = Amount required or results in future due to interest
 N,n = Number of periods a loan is in affect
     i = Interest rate, %
     I = Total interest charge over N periods,$

From previous example:

   P = $1000              i = 10%  
   F = $1500              I= F- P= 1500-1000 = 500   

Hence F = P + I   &   I = PiN = (1000)(0.10)(5) = 500  

Hence  F = P + PiN = P(1 + iN)

 

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Added to the Web: May 20, 2002.
Last updated: April 26, 2002.
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