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Texas A&M University College of Engineering

Class 3

Posted on July 27, 2021 by Abigail Stason

Learning Objectives – Class 3

After today’s lecture, and after working the homework problems, the student should be able to

  • Work problems involving gradient cash flows
  • Work problems involving geometric gradient cash flows
  • Work problems involving continuous compounding
  • Be able to work problems involving capitalized costs

Topics covered in today’s class

  1. Nominal vs. true (or effective or actual) interest rate
  2. Continuous compounding
  3. Resolving non-standard cash flows to a standard cash flow
  4. Capitalized costs
  5. Solving for P, F, i, and n in problems
  6. How much interest will I pay if the loan goes to term?
  7. How much interest will I pay if I pay off the loan at the end of the 5th year of the 30 year loan?
  8. How much interest will I pay if I increase the monthly payments made to the lender?
  9. How long will I pay if I double the monthly payments made to the lender?
  10. Emphasize that when a bank says 6% interest, they mean 6% nominal per year, not 6% per month, not 6% per day, not anything else!

For a one year loan:  F = P(1 + rnominalperyear/m)m
ieffective = (F – P) / P = [P(1 + rnominalperyear/m )m – P] / P  =  (1+rnominalperyear/m)m – 1

rnominalperyear = nominal yearly interest rate on door of bank; m = number of compounding periods per year

rtrue per compounding period = reffective per compounding period = ractual per compounding period = rnominal per year/number of compounding periods per year

For a “n” year loan:  F = P(1 + rnominal/m)mn

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