Engineering Economics Blog

  
(a)    Calculate the amount deposited 1 year ago to have $1000 now at an interest rate of 5% per year. 
  
(b)    Calculate the amount of interest earned during this time period.  

 Solution 

 (a)    The total amount accrued ($1000) is the sum of the original deposit and the earned interest.

If   X  is the original deposit,
 
  Total  accrued = deposit + deposit(interest rate) 
  $1000 =  X  +  X (0.05) =  X (1 + 0.05) = 1.05 X   

The original deposit is


  
(b)    Apply Equation [1.3] to determine the interest earned.
  
 Interest = $1000 - 952.38 = $47.62

In Examples 1.3 to 1.5 the interest period was 1 year, and the interest amount was calculated at the end of one period. When more than one interest period is involved, e.g., the amount of interest after 3 years, it is necessary to state whether the interest is accrued on a   simple  or   compound  basis from one period to the next. This topic is covered later in this chapter.
 
Since   infl  ation   can  signifi  cantly increase an interest rate, some comments about the fundamentals of infl ation are warranted at this early stage. By defi  nition, infl  ation represents a decrease in the value of a given currency. That is, $10 now will not purchase the same amount of gasoline for your car (or most other things) as $10 did 10 years ago. The changing value of the currency affects market interest rates.

In simple terms, interest rates refl ect two things: a so-called real rate of return   plus  the  expected infl  ation rate. The real rate of return allows the investor to purchase more than he or she could have purchased before the investment, while infl ation raises the real rate to the market rate that we use on a daily basis.
 
The safest investments (such as government bonds) typically have a 3% to 4% real rate of return built into their overall interest rates. Thus, a market interest rate of, say, 8% per year on a bond means that investors expect the infl  ation rate to be in the range of 4% to 5% per year.

Clearly, infl ation causes interest rates to rise.
 
 From the borrower’s perspective, the rate of infl ation is another interest rate   tacked on to the real interest rate . And from the vantage point of the saver or investor in a fi  xed-interest account, infl  ation   reduces the real rate of return  on the investment. Infl  ation means that cost and revenue cash fl ow estimates increase over time. This increase is due to the changing value of money that is forced upon a country’s currency by infl ation, thus making a unit of currency (such as the dollar) worth less relative to its value at a previous time. We see the effect of infl ation in that money purchases less now than it did at a previous time. Inflation contributes to
   •     A reduction in purchasing power of the currency
   •     An increase in the CPI (consumer price index)
   •     An increase in the cost of equipment and its maintenance
   •     An increase in the cost of salaried professionals and hourly employees
   •     A reduction in the real rate of return on personal savings and certain corporate investments

In other words, infl ation can materially contribute to changes in corporate and personal economic analysis.
  
Commonly, engineering economy studies assume that infl ation affects all estimated values equally. Accordingly, an interest rate or rate of return, such as 8% per year, is applied throughout the analysis without accounting for an additional infl ation rate. However, if infl ation were explicitly taken into account, and it was reducing the value of money at, say, an average of 4% per year, then it would be necessary to perform the economic analysis using an infl ated interest rate. (The rate is 12.32% per year using the relations derived in Chapter 14.)