Financial mathematical equivalences

As mentioned, money has value throughout time. If you want a loan for some specific time period—say 1 month— then you need to pay interest to use, for your own benefit, this money for 1 month. For example, if you want a loan of L for 1 month and the interest rate is r % per month (compound interest), then after 1 month you need to return Lp to the lender, where the financial mathematical equivalence between L and Lp is... 

In words, in this case, the future value (Lp) is equivalent to the present value (L) multiplied by 1 plus the interest rate divided by 100 (because the interest rate was given as a percentage) with an exponent equal to 1 because the loan was for 1 month. If the interest rate is given in decimal form, then the financial mathematical equivalence between Lp and L is... 

Keeping things simple, we will basically use two financial mathematical equivalences and the concepts of net present value (sometimes called net present worth) and annual equivalent benefits (or annual equivalent cost) (Sect. 12.6) to do all calculations for real-Ufe problems and project evaluations. Although it represents a limitation (not using more concepts and equations), you will be amazed at the wide variety of real-life and engineering problems that can be solved with these few rather elementary tools. Thus, we continue to meet our objectives, which are to (a) teach just a few concepts and (b) captivate you with the diversity of problematic situations that arise in process and bioprocess engineering. 

We have already described and analyzed all the financial mathematical tools needed for our calculations to fulfill the purpose of the chapter. Using these basic tools, we now introduce two concepts that are important for comparison and decision among alternatives (real-life situations and engineering projects). First, the net present value is one of the most common tools to economically evaluate projects. One of the limitations of NPV is when you are comparing two or more projects with different lifespans. Although this difficulty can be remedied, it could be cumbersome. Second, the annual equivalent benefits/costs has the advantage over NPV that you can compare projects with different lifespans. 

The program does not involve transfer credit. Both US universities have their students enroll in course numbers at their home university with course content equivalent to that to be taught at Bristol. This facilitates the use of student financial aid (scholarships and loans) since students cannot apply for financial aid for transfer credit. Students will enroll in two courses worth six credit hours, which is a full load for a summer term at both ofthe US universities. Also students participating in the program will normally have a Junior class rank. This ensures they have the mathematics and sciences background to be successful in the program. 

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