HP 12c Owners Manual

							  Section 11: Multiple Programs  121 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 121 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 1: 
Assuming that program memory still contains the last program from 
the preceding section (which consisted of 17 program lines), store after that 
program the office-supplies program from Section 8 (page 88). Since this is the 
second program to be stored in program memory, we’ll ensure that a i
00 
instruction separates it from the first program by doing step 3 in the procedure 
above. Furthermore, since this program does not end with a loop, we’ll do steps 5 
and 6 too. 
Keystrokes Display   
fs 
00- Sets calculator to Program mode.   
gi.17 
17- 43, 33   02 Sets calculator to last line keyed into 
program memory. 
gi00 
18- 43, 33   00 Ensures that second program is 
separated from first by i
00. 
\ 
19-    36 
2 20-    2 
5 21-    5 
b 22-    25 
- 23-    30 
5 24-    5 
+ 25-    40 
Keys in program. 
t 
26-    31 Halts program execution. 
gi19 
27- 43, 33   19 Branches to beginning of program. 
fs 
12,000.00 Sets calculator back to Run mode. 
(Display shown assumes results 
remain from running program in 
previous example.)  
						

							122   Section 11: Multiple Programs 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 122 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 2:
 With the two programs now stored in program memory from the 
preceding examples (occupying 27 program lines), store the amortization program 
from Section 9(page 103). Since there are already two programs stored in 
program memory, we’ll skip step 3 in the procedure above. Furthermore, since the 
amortization program ends with a loop, we’ll skip steps 5 and 6. When the 
amortization program was stored at the beginning of program memory, the i
 
instruction at the end of the program branched to the :
0 instruction in line 02. 
Since the :
0 instruction is now in line 29, we’ll specify that line number with the 
i
 instruction in line 34. 
Keystrokes Display  
fs 
00- Sets calculator to Program 
mode.  
gi.27 
27- 43, 33   19Sets calculator to last line keyed 
into program memory. 
?0 
28-  44  0
:0 29-  45  0
f! 30-  42  11
gu 31-  43  31
~ 32-    34
gu 33-  43  31
gi29 34- 43, 33   29
Keys in program 
Running Another Program   
To run a program that does not begin with program line 01: 
1. Press fs to set the calculator to Run mode. If the calculator is already in 
Run mode, skip this step. 
2. Press gi followed by two digits that specify the first line of the program. 
3. Press t. 
Example:
 Run the office-supplies program, now stored in the calculator 
beginning at program line 19, for the typewriter listing for $625. 
Keystrokes Display  
fs 
12,000.00 Sets calculator to Program 
mode.  
gi19 
12,000.00 Sets calculator to first line of 
program to be executed. 
625t 
473.75 Net cost of typewriter.  
						

							 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 123 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
 
Part III 
Solutions  
						

							 
124 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 124 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
  Section 12 
Real Estate and Lending 
Annual Percentage Rate Calculations With Fees 
Borrowers are usually charged fees in connection with the issuance of a mortgage, 
which effectively raises the interest rate. The actual amount received by the 
borrower (PV) is reduced, while the periodic payments remain the same. Given the 
life or term of the mortgage, the interest rate, the mortgage amount, and the basis 
of the fee charge (how the fee is calculated), the true Annual Percentage Rate (APR) 
may be calculated. Information is entered as follows: 
1. Press g and fCLEARG. 
2.  Calculate and enter the periodic payment amount of the loan. 
a.  Key in the total number of payment periods; press n. 
b.  Key in the periodic interest rate (as a percentage); press ¼. 
c.  Key in the mortgage amount; press $.
* 
d.  To obtain the periodic payment amount, press P.* 
3.  Calculate and key in the actual net amount disbursed.
* 
z If fees are stated as a percentage of the mortgage amount (points), recall 
the mortgage amount (:$) key in the fee (percentage) rate; press 
b-$. 
z If fees are stated as a flat charge, recall the mortgage amount (:$); 
key in the fee amount (flat charge); press -$. 
z If fees are stated as a percentage of the mortgage amount plus a flat 
charge, recall the mortgage amount (:$); key in the fee 
(percentage) rate, press b-; key in the fee amount (flat charge); press 
-$. 
4. Press ¼ to obtain the interest rate per compounding period. 
5.  To obtain the annual nominal percentage rate, key in the number of periods 
per year, then press µ. 
                                                 
*  Positive for cash received; negative for cash paid out.  
						

							 Section 12: Real Estate and Lending 125 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 125 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 1:
 A borrower is charged 2 points for the issuance of his mortgage. If 
the mortgage amount is $60,000 for 30 years and the interest rate is 111/2% per 
year, with monthly payments, what true annual percentage rate is the borrower 
paying?
 (One point is equal to 1% of the mortgage amount.) 
Keystrokes Display  
g 
  
fCLEARG 
  
30gA 
360.00 Months (into n
) 
11.5gC 
0.96 Percent monthly interest rate (into i
). 
60000$ 
60,000.00 Loan amount (into PV). 
P 
–594.17 Monthly payment (calculated). 
:$2b-$ 
58,800.00 Actual amount received by borrower 
(into PV). 
¼ 
0.98 Percent monthly interest rate 
(calculated). 
12§ 
11.76 Annual percentage rate. 
Example 2:
 Using the same information as given in example 1, calculate the 
APR if the mortgage fee is $150 instead of a percentage. 
Keystrokes Display  
g 
  
fCLEARG 
  
30gA 
360.00 Months (into n
) 
11.5gC 
0.96 Percent monthly interest rate (into i
). 
60000$ 
60,000.00 Loan amount (into PV). 
P 
–594.17 Monthly payment (calculated). 
:$150-$ 
59,850.00 Effective mortgage amount (into PV). 
¼ 
0.96 Monthly interest rate (calculated). 
12§ 
11.53 Annual percentage rate.  
						

							126  Section 12: Real Estate and Lending 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 126 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 3:
 Again using the information given in example 1, what is the APR if 
the mortgage fee is stated as 2 points plus $150?
 
Keystrokes Display  
g 
  
fCLEARG 
  
30gA 
360.00 Months (into n) 
11.5gC 
0.96 Percent monthly interest rate (into i
). 
60000$ 
60,000.00 Loan amount (into PV). 
P 
–594.17 Monthly payment (calculated). 
:$2b- 
58,800.00  
150-$ 
58,650.00 Effective mortgage amount (into PV). 
¼ 
0.98 Monthly interest rate (calculated). 
12§ 
11.80 Annual percentage rate. 
Price of a Mortgage Traded at a Discount or Premium 
Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a 
premium) than the remaining balance of the loan at the time of purchase. Given 
the amount of the mortgage, the periodic payment, the timing and amount of the 
balloon or prepayment, and the desired yield rate, the price of the mortgage may 
be found. It should be noted that the balloon payment amount (if it exists) occurs 
coincident with, and does not include, the last periodic payment amount. 
Information is entered as follows: 
1. Press g and fCLEARG. 
2.  Key in the total number of periods until the balloon payment or prepayment 
occurs; press n. (If there is no balloon payment, key in total number of 
payments and press n.) 
3.  Key in the desired periodic interest rate (yield) and press ¼. 
4.  Key in the periodic payment amount; press P.
* 
5.  Key in the balloon payment amount and press M.
* (If there is no balloon 
payment, go to step 6.) 
6. Press $ to obtain the purchase price of the mortgage. 
                                                 
*  Positive for cash received; negative for cash paid out.  
						

							 Section 12: Real Estate and Lending 127 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 127 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Example 1:
 A lender wishes to induce the borrower to prepay a low interest rate 
loan. The interest rate is 5% with 72 payments remaining of $137.17 and a 
balloon payment at the end of the sixth year of $2000. If the lender is willing to 
discount the future payments at 9%, how much would the borrower need to prepay 
the note?
 
Keystrokes Display  
g 
fCLEARG 
72n 
 
 
72.00  
 
Months (into n). 
9gC 
0.75 Discount rate (into i
). 
137.17P
* 137.17 Monthly payments (into PMT). 
2000M$ 
–8,777.61 Amount necessary to prepay the 
note. 
Example 2:
 A 9
1/2% mortgage with 26 years remaining and a remaining 
balance of $49,350 is available for purchase. Determine the price to pay for this 
mortgage if the desired yield is 12%. (Since the payment amount is not given, it 
must be calculated.) 
Keystrokes Display  
g 
fCLEARG 
26gA 
 
 
312.00  
 
Months (into n
). 
9.5gC 
0.79 Percent monthly interest rate (into i
). 
49350Þ$P 
427.17 Monthly payment to be received 
(calculated). 
12gC 
1.00 Desired monthly interest rate (into i
). 
$ 
–40,801.57 Purchase price to achieve the 
desired yield (calculated). 
                                                 
* Note that the payments are positive because this problem in seen from the viewpoint of the 
lender who will be receiving payments. The negative PV indicates money that was lent out.  
						

							128  Section 12: Real Estate and Lending 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 128 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Yield of a Mortgage Traded at a Discount or Premium 
The annual yield of a mortgage bought at a discount or premium can be 
calculated given the original mortgage amount, interest rate, and periodic 
payment, as well as the number of payment periods per year, the price paid for 
the mortgage, and the balloon payment amount (if it exists). 
Information is entered as follows: 
1. Press g and fCLEARG. 
2.  Key in the total number of periods until the balloon payment occurs and 
press n. (If there is no balloon payment, key in the total number of periods 
and press n.) 
3.  Key in the periodic payment amount then press P.
* 
4.  Key in the purchase price of the mortgage then press $.
* 
5.  Key in the balloon payment amount then press M.
* (If there is no balloon 
payment, go to step 6.) 
6. Press ¼ to obtain the yield per period. 
7.  Key in the number of periods per year and press § to obtain the nominal 
annual yield. 
Example 1: 
An investor wishes to purchase a $100,000 mortgage taken out at 
9% for 21 years. Since the mortgage was issued, 42 monthly payments have been 
made. What would be the annual yield if the purchase price of the mortgage is 
$79,000?
 (Since PMT was not given, it must be calculated). 
Keystrokes Display  
g 
fCLEARG 
21gA 
 
 
252.00  
 
Enter the number of periods (into 
n
). 
9gC 
0.75 Monthly interest rate (into i
). 
100000Þ$ 
–100,000.00Mortgage amount (into PV; 
negative to indicate money paid 
out). 
P 
884.58 Payment received (calculated). 
:n 
252.00 Recall number of periods. 
42-n 
210.00 Number of periods left after 
mortgage is bought (into n). 
                                                 
*  Positive for cash received; negative for cash paid out.    
						

							 Section 12: Real Estate and Lending 129 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 129 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
79000Þ$ 
–79,000.00 Input price of mortgage (into PV; 
negative to indicate money paid 
out). 
¼ 
0.97 Yield per month (calculated). 
12§ 
11.68 Percent annual yield. 
Example 2:
 Using the same information given in example 1, calculate the annual 
yield if the loan is to be paid in full at the end of the fifth year (from original 
issuance). (In this case both the payment amount and the balloon must be 
calculated since they are not given.) 
Keystrokes Display  
g 
fCLEARG 
21gA 
 
 
252.00  
 
Input the number of periods (into 
n). 
9gC 
0.75 Monthly interest rate (into PV). 
100000Þ$ 
–100,000.00Mortgage amount (into PV). 
P 
884.58 Payment (calculated). 
 
Calculate the remaining balance of the loan after five years. 
5gA 
60.00 Number of periods to be 
amortized. 
M 
89,849.34 Remaining balance of the loan 
after five years. 
:n 
60.00  
42-n 
18.00 New life of loan. 
79000Þ$¼ 
1.77 Percent monthly yield. (calculated). 
12§ 
21.29 Percent annual yield.  
						

							130  Section 12: Real Estate and Lending 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 130 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
The Rent or Buy Decision 
The question of whether to rent or purchase a residence is not always easy to 
answer, especially when the time period over which you would own or rent a 
house is short. This program performs an analysis which could be helpful in 
reaching a decision. Essentially, it calculates a yield or rate of return on the 
proposed investment. This yield may be compared with the yield obtained by 
renting a residence and investing the down payment and monthly payment 
differences in a savings account or other investment opportunity. This program 
takes into account the tax advantages obtained by a home owner on property 
taxes and mortgage interest. 
First the program computes the Net Cash Proceeds upon Resale (NCPR),
* next the 
yield on the investment in the house and then the value of the hypothetical savings 
account at the end of the investment period. A comparison of the NCPR and the 
final balance of the savings account and a comparison of the yields should aid in 
determining whether to rent or buy. 
KEYSTROKES DISPLAY KEYSTROKES DISPLAY 
fs  M 33-    15 
fCLEARÎ 00- t 34-    31 
M 01-    15d 35-       33 
M† 02-    15:n 36-  45  11 
:7 03-  45   7z 37-    10 
b 04-    25:4 38-  45   4 
- 05-    30- 39-    30 
:n 06-  45  11:.0 40-45  48   0 
?0 07-  44   0b 41-    25 
:$ 08-  45  13:P 42-  45  14 
fCLEARG 09-  42  34:4 43-  45   4 
                                                 
*  The Net Cash Proceeds upon Resale (NCPR = sales price – commission – mortgage balance), 
is the pre-tax proceeds. The program assumes that the buyer reinvests in like property and is 
not subject to capital gains tax. 
†  FV is repeated in the program twice to ensure that it is computed and not stored.