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
- Nominal vs. true (or effective or actual) interest rate
- Continuous compounding
- Resolving non-standard cash flows to a standard cash flow
- Capitalized costs
- Solving for P, F, i, and n in problems
- How much interest will I pay if the loan goes to term?
- How much interest will I pay if I pay off the loan at the end of the 5th year of the 30 year loan?
- How much interest will I pay if I increase the monthly payments made to the lender?
- How long will I pay if I double the monthly payments made to the lender?
- 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