#### 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 + 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}