HP 12c Owners Manual

							  Section 2: Percentage and Calendar Functions  31 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 31 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
14.052004\ 
14.05 Keys in date and separates it from 
number of days to be entered. 
120gD 
11,09,2004 6The expiration date is 11 September 
2004, a Saturday. 
When D
 is executed as an instruction in a running program, the calculator 
pauses for about 1 second to display the result, then resumes program execution. 
Number of Days Between Dates 
To calculate the number of days between two given dates: 
1.  Key in the earlier date and press \. 
2.  Key in the later date and press gÒ.
 
The answer shown in the display is the actual number of days between the two 
dates, including leap days (the extra days occurring in leap years), if any. In 
addition, the hp 12c also calculates the number of days between the two dates on 
the basis of a 30-day month. This answer is held inside the calculator; to display it, 
press ~
. Pressing ~
 again will return the original answer to the display. 
Example: 
Simple interest calculations can be done using either the actual number 
of days or the number of days counted on the basis of a 30-day month. What 
would be the number of days counted each way, to be used in calculating the 
simple interest accruing from June 3, 2004 to October 14, 2005?
 Assume that 
you normally express dates in the month-day-year format. 
Keystrokes Display  
gÕ 
11.09 Sets date format to month-day-year. 
(Display shown assumes date remains 
from preceding example.) 
6.032004\ 
6.03 Keys in earlier date and separates it 
from the later date. 
10.142005gÒ 
498.00 Keys in later date. Display shows 
actual number of days. 
~ 
491.00 Number of days counted on the basis 
of a 30-day month. 
  
						

							 
32 
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  Section 3 
Basic Financial Functions 
The Financial Registers 
In addition to the data storage registers discussed on page 23, the hp 12c has five 
special registers in which numbers are stored for financial calculations. These 
registers are designated n, i, PV, PMT, and FV. The first five keys on the top row of 
the calculator are used to store a number from the display into the corresponding 
register, to calculate the corresponding financial value and store the result into the 
corresponding register, or to display the number stored in the corresponding 
register.
*  
Storing Numbers Into the Financial Registers 
To store a number into a financial register, key the number into the display, then 
press the corresponding key (n
, ¼
, $
, P
, or M
). 
Displaying Numbers in the Financial Registers 
To display a number stored in a financial register, press :
 followed by the 
corresponding key.
† 
                                                 
* Which operation is performed when one of these keys is pressed depends upon the last 
preceding operation performed: If a number was just stored into a financial register (using 
n, ¼, $, P, M, A, or C), pressing one of these five keys calculates the 
corresponding value and stores it into the corresponding register; otherwise pressing one of 
these five keys merely stores the number from the display into the corresponding register. 
† It’s good practice to press the corresponding key twice after :, since often you may want 
to calculate a financial value right after displaying another financial value. As indicated in 
the preceding footnote, if you wanted to display FV and then calculate PV, for example, you 
should press :MM$. If you didn’t press M the second time, pressing $ would 
store FV in the PV register rather than calculating PV, and to calculate PV you would have to 
press $ again.  
						

							  Section 3: Basic Financial Functions  33 
 
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Clearing the Financial Registers 
Every financial function uses numbers stored in several of the financial registers. 
Before beginning a new financial calculation, it is good practice to clear all of the 
financial registers by pressing f
CLEARG
. Frequently, however, you may want 
to repeat a calculation after changing a number in only one of the financial 
registers. To do so, do not press f
CLEARG
; instead, simply store the new 
number in the register. The numbers in the other financial registers remain 
unchanged.  
The financial registers are also cleared when you press f
CLEARH
 and when 
Continuous Memory is reset (as described on page 70). 
Simple Interest Calculations 
The hp 12c simultaneously calculates simple interest on both a 360-day basis and 
a 365-day basis. You can display either one, as described below. Furthermore, 
with the accrued interest in the display, you can calculate the total amount 
(principal plus accrued interest) by pressing +
. 
1.  Key in or calculate the number of days, then press n. 
2.  Key in the annual interest rate, then press ¼. 
3.  Key in the principal amount, then press Þ$.
* 
4. Press fÏ to calculate and display the interest accrued on a 360-day 
basis. 
5.  If you want to display the interest accrued on a 365-day basis, press 
d~. 
6. Press + to calculate the total of the principal and the accrued interest now 
in the display. 
The quantities n, i, and PV can be entered in any order. 
Example 1:
 Your good friend needs a loan to start his latest enterprise and has 
requested that you lend him $450 for 60 days. You lend him the money at 7% 
simple interest, to be calculated on a 360-day basis. What is the amount of 
accrued interest he will owe you in 60 days, and what is the total amount owed?
 
Keystrokes Display  
60n 
60.00 Stores the number of days. 
                                                 
* Pressing the $ key stores the principal amount in the PV register, which then contains the 
present value of the amount on which interest will accrue. The Þ key is pressed first to 
change the sign of the principal amount before storing it in the PV register. This is required by 
the cash flow sign convention, which is applicable primarily to compound interest 
calculations.
  
						

							34  Section 3: Basic Financial Functions 
 
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Keystrokes Display  
7¼ 
7.00 Stores the annual interest rate. 
450Þ$ 
–450.00 Stores the principal. 
fÏ 
5.25 Accrued interest, 360-day basis. 
+ 
455.25 Total amount: principal plus accrued 
interest. 
Example 2:
 Your friend agrees to the 7% interest on the loan from the preceding 
example, but asks that you compute it on a 365-day basis rather than a 360-day 
basis. What is the amount of accrued interest he will owe you in 60 days, and 
what is the total amount owed?
 
Keystrokes Display  
60n 
7¼ 
450Þ$ 
60.00 
7.00 
–450.00If you have not altered the numbers in 
the n, i, and PV registers since the 
preceding example, you may skip 
these keystrokes. 
fÏd~ 
5.18 Accrued interest, 365-day basis. 
+ 
455.18 Total amount: principal plus accrued 
interest. 
Financial Calculations and the Cash Flow Diagram 
The concepts and examples presented in this section are representative of a wide 
range of financial calculations. If your specific problem does not appear to be 
illustrated in the pages that follow, don’t assume that the calculator is not capable 
of solving it. Every financial calculation involves certain basic elements; but the 
terminology used to refer to these elements typically differs among the various 
segments of the business and financial communities. All you need to do is identify 
the basic elements in your problem, and then structure the problem so that it will 
be readily apparent what quantities you need to tell the calculator and what 
quantity you want to solve for. 
An invaluable aid for using your calculator in a financial calculation is the cash 
flow diagram. This is simply a pictorial representation of the timing and direction 
of financial transactions, labeled in terms that correspond to keys on the calculator. 
The diagram begins with a horizontal line, called a time line. It represents the 
duration of a financial problem, and is divided into compounding periods. For 
example, a financial problem that transpires over 6 months with monthly 
compounding would be diagrammed like this:  
						

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The exchange of money in a problem is depicted by vertical arrows. Money you 
receive is represented by an arrow pointing up from the point in the time line when 
the transaction occurs; money you pay out is represented by an arrow pointing 
down. 
 
Suppose you deposited (paid out) $1,000 into an account that pays 6% annual 
interest and is compounded monthly, and you subsequently deposited an 
additional $50 at the end of each month for the next 2 years. The cash flow 
diagram describing the problem would look like this: 
 
The arrow pointing up at the right of the diagram indicates that money is received 
at the end of the transaction. Every completed cash flow diagram must include at 
least one cash flow in each direction. Note that cash flows corresponding to the 
accrual of interest are not represented by arrows in the cash flow diagram. 
The quantities in the problem that correspond to the first five keys on the top row of 
the keyboard are now readily apparent from the cash flow diagram. 
z n is the number of compounding periods. This quantity can be expressed in 
years, months, days, or any other time unit, as long as the interest rate is 
expressed in terms of the same basic compounding period. In the problem 
illustrated in the cash flow diagram above, n = 2 × 12.  
						

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The form in which n is entered determines whether or not the calculator 
performs financial calculations in Odd-Period mode (as described on pages 
50 through 53). If n is a noninteger (that is, there is at least one nonzero 
digit to the right of the decimal point), calculations of i, PV, PMT, and FV are 
performed in Odd-Period mode. 
z i is the interest rate per compounding period. The interest rate shown in the 
cash flow diagram and entered into the calculator is determined by dividing 
the annual interest rate by the number of compounding periods. In the 
problem illustrated above, i = 6% ÷ 12. 
z PV — the present value — is the initial cash flow or the present value of a 
series of future cash flows. In the problem illustrated above, PV is the $1,000 
initial deposit. 
z  PMT is the period payment. In the problem illustrated above PMT is the $50 
deposited each month. When all payments are equal, they are referred to as 
annuities. (Problems involving equal payments are described in this section 
under Compound Interest Calculations; problems involving unequal 
payments can be handled as described in under Discounted Cash Flow 
Analysis: NPV and IRR. Procedures for calculating the balance in a savings 
account after a series of irregular and/or unequal deposits are included in 
the hp 12c Solutions Handbook.) 
z FV — the future value — is the final cash flow or the compounded value of a 
series of prior cash flows. In the particular problem illustrated above, FV is 
unknown (but can be calculated). 
Solving the problem is now basically a matter of keying in the quantities identified 
in the cash flow diagram using the corresponding keys, and then calculating the 
unknown quantity by pressing the corresponding key. In the particular problem 
illustrated in the cash flow diagram above, FV is the unknown quantity; but in other 
problems, as we shall see later, n, i, PV, or PMT could be the unknown quantity. 
Likewise, in the particular problem illustrated above there are four known 
quantities that must be entered into the calculator before solving for the unknown 
quantity; but in other problems only three quantities may be known — which must 
always include n or i. 
The Cash Flow Sign Convention 
When entering the PV, PMT, and FV cash flows, the quantities must be keyed into 
the calculator with the proper sign, + (plus) or – (minus), in accordance with … 
The Cash Flow Sign Convention: Money received (arrow pointing up) 
is entered or displayed as a positive value (+). Money paid out (arrow 
pointing down) is entered or displayed as a negative value (–).  
						

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The Payment Mode 
One more bit of information must be specified before you can solve a problem 
involving periodic payments. Such payments can be made either at the beginning 
of a compounding period (payments in advance, or annuities due) or at the end of 
the period (payments in arrears, or ordinary annuities). Calculations involving 
payments in advance yield different results than calculations involving payments in 
arrears. Illustrated below are portions of cash flow diagrams showing payments in 
advance (Begin) and payments in arrears (End). In the problem illustrated in the 
cash flow diagram above, payments are made in arrears. 
 
Regardless of whether payments are made in advance or in arrears, the number of 
payments must be the same as the number of compounding periods. 
To specify the payment mode: 
z  Press g× if payments are made at the beginning of the compounding 
periods.  
z  Press g if payments are made at the end of the compounding periods. 
The BEGIN
 status indicator is lit when the payment mode is set to Begin. If BEGIN
 
is not lit, the payment mode is set to End.   
The payment mode remains set to what you last specified until you change it; it is 
not reset each time the calculator is turned on. However, if Continuous Memory is 
reset, the payment mode will be set to End. 
Generalized Cash Flow Diagrams 
Examples of various kinds of financial calculations, together with the applicable 
cash flow diagrams, appear under Compound Interest Calculations later in this 
section. If your particular problem does not match any of those shown, you can 
solve it nevertheless by first drawing a cash flow diagram, then keying the 
quantities identified in the diagram into the corresponding registers. Remember 
always to observe the sign convention when keying in PV, PMT, and FV. 
The terminology used for describing financial problems varies among the different 
segments of the business and financial communities. Nevertheless, most problems 
involving compound interest can be solved by drawing a cash flow diagram in 
one of the following basic forms. Listed below each form are some of the problems 
to which that diagram applies.  
						

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Compound Interest Calculations 
Specifying the Number of Compounding Periods and the Periodic 
Interest Rate 
Interest rates are usually quoted at the annual rate (also called the nominal rate): 
that is, the interest rate per year. However, in compound interest problems, the 
interest rate entered into i must always be expressed in terms of the basic 
compounding period, which may be years, months, days, or any other time unit. 
For example, if a problem involves 6% annual interest compounded quarterly for 5 
years, n — the number of quarters — would be 5 × 4 = 20 and i — the interest 
rate per quarter — would be 6% ÷ 4 = 1.5%. If the interest were instead 
compounded monthly, n would be 5 × 12 = 60 and i would be 6% ÷ 12 = 0.5%. 
If you use the calculator to multiply the number of years by the number of 
compounding periods per year, pressing n
 then stores the result into n
. The same 
is true for i
. Values of n and i are calculated and stored like this in Example 2 on 
page 47. 
If interest is compounded monthly, you can use a shortcut provided on the 
calculator to calculate and store n and i: 
z  To calculate and store n, key the number of years into the display, then press 
gA. 
z  To calculate and store i, key the annual rate into the display, then press 
gC. 
Note that these keys not only multiply or divide the displayed number by 12; they 
also automatically store the result in the corresponding register, so you need not 
press the n
 or ¼
 key next. The A
 and C
 keys are used in Example 1 on 
page 46. 
Calculating the Number of Payments or Compounding Periods 
1. Press fCLEARG to clear the financial registers. 
2.  Enter the periodic interest rate, using ¼ or C. 
3.  Enter at least two of the following values: 
z Present value, using $. 
z Payment amount, using P. 
z Future value, using M.  Note: 
Remember to observe 
the cash flow sign convention. 
4. If a PMT was entered, press g× or g to set the payment mode. 
5. Press n to calculate the number of payments or periods.  
						

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If the answer calculated is not an integer (that is, there would be nonzero digits to 
the right of the decimal point), the calculator rounds the answer up to the next 
higher integer before storing it in the n register and displaying it.
*  For example, if 
n were calculated as 318.15, 319.00
 would be the displayed answer.   
n is rounded up by the calculator to show the total number of payments needed: 
n–1 equal, full payments, and one final, smaller payment. The calculator does not 
automatically adjust the values in the other financial registers to reflect n equal 
payments; rather, it allows you to choose which, if any, of the values to adjust.
† 
Therefore, if you want to know the value of the final payment (with which you can 
calculate a balloon payment) or desire to know the payment value for n equal 
payments, you will need to press one of the other financial keys, as shown in the 
following two examples. 
Example 1: 
You’re planning to build a log cabin on your vacation property. 
Your rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325 
payments at the end of each month, how many payments will be required to pay 
off the loan, and how many years will this take?
 
 
Keystrokes Display  
fCLEARG 
10.5gC 
 
0.88  
Calculates and stores i. 
35000$ 
35,000.00Stores PV. 
325ÞP 
–325.00 Stores PMT (with minus sign for cash 
paid out). 
g 
–325.00 Sets the payment mode to End. 
n 
328.00 Number of payments required. 
                                                 
* The calculator will round n down to the next lower integer if the fractional portion of n is less 
than 0.005. 
† After calculating n, pressing ¼, $, P, or M will recalculate the value in the 
corresponding financial register.