Class 3

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 + r_{nominalperyear}/m)^m
i_effective = (F – P) / P = [P(1 + r_{nominalperyear}/m )^m – P] / P  =  (1+r_{nominalperyear}/m)^m – 1

r_{nominalperyear} = nominal yearly interest rate on door of bank; m = number of compounding periods per year

r_{true per compounding period} = r_{effective per compounding period} = r_{actual per compounding period} = r_{nominal per year}/number of compounding periods per year

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