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Picturing Financial Problems58
• 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.
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 30-year,
150,000.00 mortgage, with a payment of 1,041.40, at 7.5% annual interest, with a 10,000
balloon payment.
Table 5-1 Keys for solving a TVM problem
Keys Description
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).
- User’s Guide 1
- Legal Notice 2
- Keyboard Map Legend 4
- Table of Contents 5
- 1 At a Glance 9
- Shift Keys 10
- Boxed Key Functions 10
- Percentages 11
- Memory Keys 12
- At a Glance 13
- Time Value of Money (TVM) 14
- TVM What if 15
- Amortization 16
- Depreciation 17
- Interest Rate Conversion 18
- ¤ enters a cash flow 19
- ¤ to enter cash 19
- 1 or A to 19
- 1 to scroll through the 20
- Date and Calendar 21
- At a Glance...14 22
- Break-even 24
- 1 to scroll 26
- M to exit 26
- Probability 27
- Trigonometric Functions 28
- Keys Display Description 29
- At a Glance...22 30
- 2 Getting Started 31
- Basics of Key Functions 32
- Operating Modes 34
- Arithmetic Operators 34
- Calculations in Chain Mode 35
- J1GPD4 returns a 36
- D:a\qgVA 36
- Clearing the Calculator 37
- Annunciators 38
- Getting Started 39
- Input Key 40
- Swap Key 40
- Statistics Keys 40
- Math Functions 41
- Getting Started34 42
- Selecting Angle Format 43
- Hyperbolic Functions 44
- Two-Number Functions 45
- In-line Functions 45
- Getting Started38 46
- Getting Started40 48
- Last Answer 49
- Display Format of Numbers 49
- Getting Started42 50
- Scientific Notation 51
- Rounding Numbers 51
- Messages 52
- § key has two functions: 53
- Percent Change 54
- Margin Calculations 55
- Markup on Cost Calculations 55
- Business Percentages48 56
- Using Constants 57
- Using the M Register 59
- Using Numbered Registers 60
- É (future 63
- Signs of Cash Flows 64
- Periods and Cash Flows 64
- Simple and Compound Interest 64
- Interest Rates 65
- Recognizing a TVM Problem 66
- Picturing Financial Problems 67
- \½ (Net Present Value) or \Á 68
- Using the TVM Application 69
- The TVM Keys 69
- Begin and End Modes 70
- Loan Calculations 70
- Savings Calculations 75
- Lease Calculations 79
- JV:::yÉ 82
- To Amortize 83
- Amortize the 1 86
- , and 54 86
- payments 86
- Resetting the TVM Keys 90
- 7Depreciation 91
- 8 Cash Flow Calculations 95
- Clearing the Cash Flow Memory 96
- Figure 1 97
- Figure 2 97
- Figure 3 97
- 3. Press \Á 98
- JJjSV7Gd¤ 99
- 12 periods per year 100
- Cash Flow Calculations 101
- Cash Flow Calculations94 102
- Cash Flow Calculations96 104
- Cash Flow Calculations98 106
- Date Format 107
- Calendar Format 107
- Using the INPUT key 108
- Date Calculation 109
- Number of Days 110
- Example 2 111
- J:7JjG:JGÆ 112
- S7:YG:JV\Ä 112
- 10 Bonds 113
- Example 1 114
- Resetting the bond keys 116
- 11 B r e a k - e v e n 117
- ]OY. A brief message 120
- 12 Statistical Calculations 121
- Clearing Statistical Data 122
- Entering Statistical Data 122
- One-Variable Statistics 123
- Statistical Calculations 125
- YDÆJ:GD¡ 126
- DjÆSgV¡ 126
- \«Displays: 127
- Statistical Calculations120 128
- Statistical Calculations122 130
- Weighted Mean 132
- \Z, \W, or 134
- Combinations 135
- Random Number and Seed 135
- Statistical Calculations128 136
- Normal Lower Tail Probability 137
- 7:GV]oF 138
- Example: 139
- GS]oI7:V4 140
- GSÆ7:V]oI 140
- Conversions from Lower Tail 141
- Statistical Calculations136 144
- Y:::::a 145
- G:aJ::4 145
- Additional Examples138 146
- Loans and Mortgages 147
- Additional Examples140 148
- Additional Examples 149
- Additional Examples142 150
- Additional Examples144 152
- Automobile Loan 153
- Canadian Mortgages 154
- What if … TVM Calculations 155
- Saving for College Costs 156
- Additional Examples150 158
- Cash Flow Examples 160
- Net Future Value 162
- Power and Batteries 163
- Low Power Annunciator 163
- Installing Batteries 163
- The calculator won’t turn on: 164
- Resetting the calculator: 164
- \8 (Ch. 2 Getting Started) 165
- Environmental Limits 166
- IRR/YR Calculations 167
- Equations 167
- Interest Rate Conversions 168
- Forecasting 172
- Appendix C: Messages 173
- Table C-1 Messages 174
- Message Displayed Description 174
- Replacing the Batteries 175
- General Terms 176
- Exclusions 176
- Regulatory Information 177
- Modifications 177
- States Only 178
- Canadian Notice 178
- Avis Canadien 178
- Japanese Notice 179
- European Union 179
- Customer Care 180
- Contact Information 180
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