•As a periodic rate. This is the rate that is applied to your money from period to period.
•As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year.
•As an annual effective rate. This is an annual rate that considers compounding.
In the previous example of a 1,000.00 savings account, the periodic rate is 1/2 % (per month),
quoted as an annual nominal rate of 6% ( 1/2 × 12). This same periodic rate could be quoted as an annual effective rate, which considers compounding. The balance after 12 months of compounding is 1,061.68, which means the annual effective interest rate is 6.168%.
Examples of converting between nominal and annual effective rates can be found in the section titled, Interest Rate Conversions in the next chapter.
Two Types of Financial Problems
The financial problems in this manual use compound interest unless specifically stated as simple interest calculations. Financial problems are divided into two groups:
•TVM problems
•Cash flow problems
Recognizing a TVM Problem
If uniform cash flows occur between the first and last periods on the cash flow diagram, the financial problem is a TVM (time value of money) problem. There are five main keys used to solve a TVM problem.
Table
KeysDescription
Ù | Number of periods or payments |
| |
|
|
Ò | Annual percentage interest rate (usually the annual nominal |
rate) | |
|
|
Ï | Present value (the cash flow at the beginning of the time |
line) | |
|
|
Ì | Periodic payment |
| |
|
|
É | Future value (the cash flow at the end of the cash flow |
diagram, in addition to any regular periodic payment). | |
|
|
You can calculate any value after entering the other four values. Cash flow diagrams for loans, mortgages, leases, savings accounts, or any contract with regular cash flows of the same amount are normally treated as TVM problems.
For example, following is a cash flow diagram, from the borrower’s perspective, for a
58 Picturing Financial Problems