HP 12c Owners Manual

							  Section 3: Basic Financial Functions  41 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 41 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
12z 
27.33 Twenty-seven years and four months. 
Because the calculator rounds the calculated value of n up to the next higher 
integer, in the preceding example it is likely that — while 328 payments will be 
required to pay off the loan — only 327 full payments of $325 will be required, 
the next and final payment being less than $325. You can calculate the final, 
fractional, 328th payment as follows:   
Keystrokes Display  
328n 
328.00 Stores total number of payments.* 
M 
181.89 Calculates FV — which equals the 
overpayment if 328 full payments 
were made. 
:P 
–325.00 Recalls payment amount. 
+ 
–143.11 Final, fractional payment. 
Alternatively, you could make the fractional payment together with the 327th 
payment. (Doing so will result in a somewhat smaller total of all payments, since 
you will not have to pay interest during the 328th payment period.) You can 
calculate this final, larger, 327th payment (essentially a balloon payment) as 
follows: 
Keystrokes Display  
327n 
327.00 Stores number of full payments. 
M 
–141.87 Calculates FV — which is the balance 
remaining after 327 full payments. 
:P 
–325.00 Recalls payment amount. 
+ 
–466.87 Final, balloon payment. 
Instead of having a fractional (or balloon) payment at the end of the loan, you 
might wish to make 327 or 328 equal payments. Refer to “Calculating the 
Payment Amount” on page 46 for a complete description of this procedure. 
                                                 
* You could skip this step, since 328 is already stored in the n register. If you do so, however, 
you will need to press M twice in the next step (for the reason discussed in the first footnote 
on page 32; you would not have to press M twice if you had not pressed 12z after w in 
the example above.) We choose to show this and the following example in a parallel format 
so that the procedure is easy to remember: the number you key is the number of the final 
payment — either the fractional payment or the balloon payment — whose amount is to be 
calculated.  
						

							42  Section 3: Basic Financial Functions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 42 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 2:
 You’re opening a savings account today (the middle of the month) 
with a $775 deposit. The account pays 61/4% interest compounded semimonthly. 
If you make semimonthly deposits of $50 beginning next month, how long will it 
take for your account to reach $4000?
 
 
Keystrokes Display  
fCLEARG 
6.25\24z¼ 
 
0.26  
Calculates and stores i. 
775Þ$ 
–775.00 Stores PV (with minus sign for cash 
paid out). 
50ÞP 
–50.00 Stores PMT (with minus sign for cash 
paid out). 
4000M 
4,000.00 Stores FV. 
g 
4,000.00 Sets the payment mode to End. 
n 
58.00 Number of semimonthly deposits. 
2z 
29.00 Number of months. 
As in Example 1, it is likely that only 57 full deposits will be required, the next and 
final deposit being less than $50. You can calculate this final, fractional, 58th 
deposit as in Example 1, except that for this example you must subtract the original 
FV. (In Example 1, the original FV was zero.) The procedure is as follows:  
						

							  Section 3: Basic Financial Functions  43 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 43 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
MM 
4,027.27 Calculates FV – which equals the 
balance in the account if 58 full 
deposits were made.
* 
:P 
–50.00 Recalls amount of deposits. 
+ 
3,977.27 Calculates the balance in the account 
if 57 full deposits were made and 
interest accrued during the 58
th 
month.† 
4000- 
–22.73 Calculates final, fractional, 58th 
deposit required to reach $4,000. 
Calculating the Periodic and Annual Interest Rates 
1. Press fCLEARG to clear the financial registers. 
2.  Enter the number of payments or periods, using n or A. 
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 si
gn 
convention. 
4. If a PMT was entered, press g× or g to set the payment mode. 
5. Press ¼ to calculate the periodic interest rate. 
6.  To calculate the annual interest rate, key in the number of periods per year, 
then press §. 
                                                 
* In this example, M must be pressed twice, since the preceding key pressed was z. If we 
had stored the number of deposits in n (as we did following Example 1), we would have to 
press M only once here, since the preceding key pressed would have been w (as it was 
following Example 1). Remember that it is not necessary to store the number of payments in n 
before calculating the amount of the final, fractional payment. (Refer to the preceding 
footnote.) 
† You might think that we could calculate the balance in the account after 57 full deposits were 
made simply by storing that number in n and then calculating FV, as we did using the second 
method following Example 1. However, this balance would not include the interest accrued 
during the 58th month.  
						

							44  Section 3: Basic Financial Functions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 44 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example: 
What annual interest rate must be obtained to accumulate $10,000 in 
8 years on an investment of $6,000 with quarterly compounding? 
 
Keystrokes   Display   
fCLEARG 
8\4§w 
 
32.00  
Calculates and stores n. 
6000Þ$ 
–6,000.00Stores PV (with minus sign for cash 
paid out). 
10000M 
10,000.00Stores FV. 
¼ 
1.61 Periodic (quarterly) interest rate. 
4§ 
6.44 Annual interest rate. 
Calculating the Present Value 
1. Press fCLEARG to clear the financial registers. 
2.  Enter the number of payments or periods, using n or A. 
3.  Enter the periodic interest rate, using ¼ or C. 
4.  Enter either or both of the following: 
z Payment amount, using P. 
z Future value, using M.  Note: 
Remember to 
observe the cash flow si
gn 
convention. 
5. If a PMT was entered, press g× or g to set the payment mode. 
6. Press $ to calculate the present value.  
						

							  Section 3: Basic Financial Functions  45 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 45 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 1: 
You’re financing a new car purchase with a loan from an institution 
that requires 15% interest compounded monthly over the 4-year term of the loan. If 
you can make payments of $150 at the end of each month and your down 
payment will be $1,500, what is the maximum price you can pay for the car?
 
(Assume the purchase date is one month prior to the date of the first payment.)   
 
Keystrokes Display  
fCLEARG 
4gA 
 
48.00  
Calculates and stores n. 
15gC 
1.25 Calculates and stores i. 
150ÞP 
–150.00 Stores PMT (with minus sign for cash 
paid out). 
g 
–150.00 Sets payment mode to End. 
$ 
5,389.72 Maximum amount of loan. 
1500+ 
6,889.72 Maximum purchase price. 
Example 2:
 A development company would like to purchase a group of 
condominiums with an annual net cash flow of $17,500. The expected holding 
period is 5 years, and the estimated selling price at that time is $540,000. 
Calculate the maximum amount the company can pay for the condominiums in 
order to realize at least a 12% annual yield. 
  
						

							46  Section 3: Basic Financial Functions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 46 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
fCLEARG 
5n 
 
5.00  
Stores n. 
12¼ 
12.00 Stores i. 
17500P 
17,500.00 Stores PMT. Unlike in the previous 
problem, here PMT is positive 
since it represents cash received. 
540000M 
540,000.00 Stores FV. 
g 
540,000.00 Sets payment mode to End. 
$ 
–369,494.09 The maximum purchase price to 
provide a 12% annual yield. PV is 
displayed with a minus sign since 
it represents cash paid out. 
Calculating the Payment Amount 
1. Press fCLEARG to clear the financial registers. 
2.  Enter the number of payments or periods, using n or A. 
3.  Enter the periodic interest rate, using ¼ or C. 
4.  Enter either or both of the following: 
z Present value, using $. 
z Future value, using M.  Note: 
Remember to 
observe the cash flow si
gn 
convention. 
5. Press g× or g to set the payment mode. 
6. Press P to calculate the payment amount. 
Example 1:
 Calculate the payment amount on a 29-year, $43,400 mortgage at 
14
1/4% annual interest. 
  
						

							  Section 3: Basic Financial Functions  47 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 47 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
fCLEARG 
29gA 
 
348.00  
Calculates and stores n. 
14.25gC 
1.19 Calculates and stores i. 
43400$ 
43,400.00 Stores PV. 
g 
43,400.00 Sets payment mode to End. 
P 
–523.99 Monthly payment (with minus sign 
for cash paid out).   
Example 2:
 Looking forward to retirement, you wish to accumulate $60,000 
after 15 years by making deposits in an account that pays 9
3/4% interest 
compounded semiannually. You open the account with a deposit of $3,200 and 
intend to make semiannual deposits, beginning six months later, from your 
profit-sharing bonus paychecks. Calculate how much these deposits should be. 
 
Keystrokes Display  
fCLEARG 
15\2µw 
 
30.00  
Calculates and stores n. 
9.75\2z¼ 
4.88 Calculates and stores i. 
3200Þ$ 
–3200.00 Stores PV (with minus sign for cash 
paid out). 
60000M 
60,000.00Stores FV. 
g 
60,000.00Sets payment mode to End. 
P 
–717.44 Semiannual payment (with minus sign 
for cash paid out).  
						

							48  Section 3: Basic Financial Functions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 48 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Calculating the Future Value 
1. Press fCLEARG to clear the financial registers. 
2.  Enter the number of payments or periods, using n or A. 
3.  Enter the periodic interest rate, using ¼ or C. 
4.  Enter either or both of the following: 
z Present value, using $. 
z Payment amount, using P.  Note: 
Remember to 
observe the cash flow si
gn 
convention. 
5. If a PMT was entered, press g× or g to set the payment mode. 
6. Press M to calculate the future value. 
Example 1:
 In Example 1 on page 46, we calculated that the payment amount 
on a 29-year, $43,400 mortgage at 14
1/4% annual interest is $523.99. If the 
seller requests a balloon payment at the end of 5 years, what would be the 
amount of the balloon?
 
 
Keystrokes Display  
fCLEARG 
5gA 
 
60.00  
Calculates and stores n. 
14.25gC 
1.19 Calculates and stores i. 
43400$ 
43,400.00Stores PV. 
523.99ÞP 
–523.99 Stores PMT (with minus sign for cash 
paid out). 
g 
–523.99 Sets payment mode to End. 
M 
–42,652.37Amount of balloon payment.  
						

							  Section 3: Basic Financial Functions  49 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 49 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 2:
 If you deposit $50 a month (at the beginning of each month) into a 
new account that pays 61/4% annual interest compounded monthly, how much will 
you have in the account after 2 years?
 
 
Keystrokes Display  
fCLEARG 
2gA 
 
24.00  
Calculates and stores n. 
6.25gC 
0.52 Calculates and stores i. 
50ÞP 
–50.00 Stores PMT (with minus sign for cash 
paid out). 
g× 
–50.00 Sets payment mode to Begin. 
M 
1,281.34 Balance after 2 years. 
Example 3:
 Property values in an unattractive area are depreciating at the rate 
of 2% per year. Assuming this trend continues, calculate the value in 6 years of 
property presently appraised at $32,000. 
 
Keystrokes Display  
fCLEARG 
6n 
 
6.00  
Stores n.  
						

							50  Section 3: Basic Financial Functions 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 50 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
2Þ¼ 
–2.00 Stores i (with minus sign for a 
“negative interest rate”). 
32000Þ $ 
–32,000.00 Stores PV (with minus sign for cash 
paid out). 
M 
28,346.96 Property value after 6 years. 
Odd-Period Calculations 
The cash flow diagrams and examples presented so far have dealt with financial 
transactions in which interest begins to accrue at the beginning of the first regular 
payment period. However, interest often begins to accrue prior to the beginning of 
the first regular payment period. The period from the date interest begins accruing 
to the date of the first payment, being not equal to the regular payment periods is 
sometimes referred to as an “odd first period”. For simplicity, in using the hp 12c 
we will always regard the first period as equal to the remaining periods, and we 
will refer to the period between the date interest begins accruing and the 
beginning of the first payment period as simply the “odd period” or the “odd 
days”. (Note that the odd period is always assumed by the calculator to occur 
before the first full payment period.) The following two cash flow diagrams 
represent transactions including an odd period for payments in advance (Begin) 
and for payments in arrears (End).