#### Learning Objectives – Class 2

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

- Determine the amount of money required to be invested to acquire a given amount of money at some time in the future.
- Know the meaning of, and be able to solve economic problems involving equivalence.
- Be able to use the rule of 72 in economics problems.
- Be able to solve problems in which sub-compounding periods are involved.
- Be able to solve problems in which continuous compounding is involved.
- Utilize and solve economic equivalence problems using any of the standard cash flow series equations.

#### Topics covered in today’s class

Emphasize drawing of cash flow diagrams

Emphasize EQUIVALENCE

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!

Derive Economic Formulas <–Print out this page and bring it to class with you.

- Move money from future to present
- Move money from present to future
- Move money from future to annual
- Move money from annual to future
- Move money from future to gradient
- Move money from gradient to future

Rule of 72 – 1% for 72 years = 2.047, 2% for 36 years = 2.039, 4% for 18 years = 2.026, 8% for 9 years = 1.999, etc.

Nominal and effective interest rate for sub-compounding periods

- $1 at 12%/year (nominal) compounded once a year: F = $1(1+0.12)^1 = $1.12, so itrue = ($1.12-$1.00)/$1.00 which is a true rate of 0.12 = 12% /year
- $1 at 12%/year (nominal) compounded every 6 months: F = $1(1+0.12/2)^2 = $1.1236 which is a true rate of 12.36% /year
- $1 at 12%/year (nominal) compounded monthly: F = $1(1+ 0.12/12)^12 = $1.126825 which is a true rate of 12.6825% /year
- $1 at 12%/year (nominal) compounded secondly: F = $1(1+ 0.12/(365*24*60*60))^(365*24*60*60) = $1.1273129 which is a true rate of 12.73129% /year

Show economics shorthand conventions: F = P[ 1 + i ] n = P [ F / P , i , n ]

Show where materials available for use on the exam can be found. <–Print this out and bring it to class with you.