This program is Copyright © 1976 by HewlettPackard and is used here by permission. This program was originally published in the HP67 Business Decisions Pac.
This program is supplied without representation or warranty of any kind. HewlettPackard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
Direct Reduction Loans Sinking Fund 

Shift 
Start 




Label 
<>n 
<>i 
<>PMT 
<>PV 
<>FV(BAL) 
Key 
A 
B 
C 
D 
E 
In the diagram above, the horizontal line represents the time period(s) involved, while the arrows represent the cash flows.
This program may be used to solve problems when payments are made at the end of the compounding periods (ordinary annuity). Direct reduction loans and mortgages are typical examples.
The following variables may be inputs or outputs:
In this program, A is used to input/calculate n, B to input/calculate i, C to input/calculate PMT, D to input/calculate PV, and E to input/calculate FV(BAL). After all inputs have been entered, it is possible to calculate the unknown value by pressing the appropriate user definable key.
When the START function (f A) is executed, it sets PMT, PV, and BAL to zero (n and i are not affected). START provides a safe, convenient, easy to remember method of preparing the calculator for a new problem. It is not necessary to use START between problems containing the same combination of variables. For instance, any number of n, i, PMT, PV problems involving different numbers and/or different combinations of known values could be done in succession without using START. Only the values which change from problem to problem would have to be keyed in. To change the combination of variables without using START, simply input zero for any variable which is no longer applicable. To go from n, i, PMT, PV problems to n, i, PMT, FV problems a zero would be input (0 D) for PV.
START should always be used immediately after loading Direct Reduction Loans/Sinking Fund.
Iterative interest solutions are accurate to the number of significant figures of the display setting. It is possible to obtain more significant figures by changing the display setting from DSP 2 to DSP 3, DSP 4, DSP 5, etc. before calculating. However, time for solution increases as accuracy is improved.
Problems with negative balloon payments may have more than one mathematically correct answer (or no answer at all). While this program may find one of the answers, it has no way of finding or indicating other possibilities.
The values for n, i, PMT, PV, and FV(BAL) are stored in registers AE respectively. They may be displayed by recalling the appropriate register.
Step 
Instructions 
Input Data/Units 
Keys 
Output Data/Units 
1 
Load side 1 and side 2. 

2 
Initialize (START) 
INV 
f A 
0.00 
3 
Input the known values: 




Number of periods 
n 
A 
n 

Periodic interest rate 
i (%) 
B 
i (%) 

Periodic payment 
PMT 
C 
PMT 

Present value 
PV 
D 
PV 

Future value, balloon payment, or balance 
FV(BAL) 
E 
FV(BAL) 
4 
Calculate the unknown value: 




Number of periods 

A 
n 

Periodic interest rate 

B 
i (%) 

Periodic payment 

C 
PMT 

Present value 

D 
PV 

Future value, balloon payment, or balance 

E 
FV(BAL) 
5 
For a new case, go to step 3 and change appropriate values. 



6 
For a new type of problem, go to step 2. 



A borrower can afford a $368.21 monthly principal and interest payment on a 30 year, 9.25% mortgage. What is the largest such mortgage he can obtain?
Keystrokes Outputs f A 368.21 C 30 ENTER 12 x A 360.00 (total monthly periods in mortgage life) 9.25 ENTER 12 ÷ B 0.77 (monthly interest rate) D 44757.63 (mortgage amount)
A 30 year, $50,000 mortgage has monthly payments of $320, including principal and interest. What is the annual percentage rate?
Keystrokes Outputs f A 30 ENTER 12 x A 50000 D 320 C B 0.55 (monthly percentage rate) 12 x 6.62 (annual percentage rate)
An investor wishes to purchase a mortgage with a balloon payment to yield him 14% per annum. What maximum price can he pay if there are 60 monthly payments of $250 and a $10,000 balloon at the end of year 5? If he purchases the mortgage for $14,500, what annual yield is he achieving?
Keystrokes Outputs f A 14 ENTER 12 ÷ B 60 A 250 C 10000 E D 15730.27 (maximum price to pay to yield 14%) 14500 D B 1.39 (monthly percent yield) 12 x 16.67 (annual % yield at $14,500 price)
You have an opportunity to purchase a $10,000, 8% note which has a term of 6 years (monthly payments). What should you pay for the note if you wish to achieve a 13% yield?
Keystrokes Outputs f A 10000 D 8 ENTER 12 ÷ B 6 ENTER 12 x A C 175.33 (monthly payment)
Now determine the purchase price of the note.
13 ENTER 12 ÷ B D 8734.26 (purchase price)
A borrower is charged 2 points for the issuance of his mortgage and note. If the mortgage amount is $60,000 for 30 years, and the interest rate is 8.75% per year, with monthly payments, what annual percentage rate (APR) is the borrower paying? (1 point is equal to 1% of the mortgage amount.)
First calculate the periodic payment amount.
Keystrokes Outputs f A 60000 D 30 ENTER 12 x A 8.75 ENTER 12 ÷ B C 472.02 (monthly payment)
Now calculate the mortgage amount less fees.
RCL D 2 %  D 58800.00 (effective amount borrowed)
To obtain the annual percentage rate, press:
B 12 x 8.97 (% APR)
You are setting up a travel fund for a trip to Australia. If you start in a month, depositing $150 per month in a 5.5% account, compounded monthly, how long will it take from today to accumulate $2500 for the trip?
Keystrokes Outputs f A 150 C 5.5 ENTER 12 ÷ B 2500 E A 16.10 months
A corporation has determined that a certain piece of equipment costing $50,000 will be required in 3 years. Assuming a fund paying 7% compounded quarterly is available, what quarterly payment amount must be placed in the fund in order to cover this cost if savings are to start at the end of this quarter?
Keystrokes Outputs f A 50000 E 3 ENTER 4 x A 7 ENTER 4 ÷ B C 3780.69 (quarterly payment)
LINE KEYS 001 *LBL A n>RA 002 STO A 003 F3? Digit entered? 004 RTN 005 GSB 0 006 RCL E 007 LST X 008  009 RCL D 010 LST X 011  012 ÷ 013 LN 014 RCL 7 015 LN 016 ÷ 017 STO A 018 RTN 019 *LBL C PMT>RC 020 STO C Digit entered? 021 F3? 022 RTN 023 1 Store dummy 1 for PMT. 024 STO C 025 GSB 0 026 1/X Solve for PMT and store in RC. 027 RCL D 028 roll up 029  030 x 031 STO C 032 RTN 033 *LBL D 034 STO D PV>RD 035 F3? Digit entered? 036 RTN 037 GSB 0 Solve for PV and store in RD. 038 + 039 STO D 040 RTN 041 *LBL E FV(BAL)>RE 042 STO E 043 F3? Digit entered? 044 RTN 045 GSB 0 046 RCL D Solve for FV(BAL) and store in RE 047 X<>Y 048  049 RCL 8 050 ÷ 051 STO E 052 RTN 053 *LBL 0 Store FV(BAL) flag. 054 CF 1 If PV=0 set FV(BAL) flag. 055 RCL D 056 X=0? 057 SF 1 058 1 i/100>R9 059 RCL B 060 % 061 STO 9 062 + (1+i)>R7 063 STO 7 064 RCL A (1+i)^{n}>R8 065 CHS 066 Y^{X} 067 STO 8 068 RCL E 069 x 1(1+i)^{n}>R4 070 1 071 RCL 8 072  Calculate +/(PMT/i) and store in R3 073 STO 4 074 RCL C 075 RCL 9 076 ÷ 077 F1? 078 CHS 079 STO 3 +/PMT/i[1(1+i)^{n}] 080 x 081 RTN 082 *LBL a Start by clearing PMT, PV, FV(BAL) registers. 083 CLX 084 STO C 085 STO D 086 STO E 087 RTN 088 *LBL B 089 STO B i>R8 090 F3? Digit entered? 091 RTN 092 0 093 STO B Clear R8 for some of i terms. 094 2 095 1 Store address of R8 in RI for indirect access. 096 STO I 097 RCL E 098 RCL A 099 RCL C 100 x Start guess of i: 101 + nPMT + FV(BAL) 102 RCL D If PV = 0 GTO FV(BAL) guess 103 X=0? 104 GTO 3 PV guess for i: 105  (nPMT+FV(BAL)PV)/n 106 RCL A 107 ÷ 108 RCL D and recall PV. 109 GTO 4 110 *LBL 3 FV(BAL) guess for i numerator: 111 RCL E 112 LST X 113  2(FV(BAL)nPMT) 114 ENTER 115 + 116 RCL A and denominator 117 1 (n1)^{2}PMT+FV(BAL) 118  119 x^{2} 120 RCL C 121 x 122 RCL E 123 + 124 *LBL 4 Guess for i 125 ÷ If guess < 0.9; use 0.9 126 . for guess 127 9 128 CHS 129 X<=Y? 130 X<>Y 131 GSB 5 132 X=0? If guess = 0 stop 133 RTN 134 *LBL 6 135 GSB 0 136 + Calculate f(i) 137 F1? 138 CHS 139 RCL D 140  141 RCL 8 142 RCL A 143 RCL 7 Calculate f'(i) 144 ÷ 145 x 146 F1? 147 CLX 148 STO 6 149 F1? 150 roll dn 151 F1? 152 LST X 153 RCL 4 154 RCL 9 155 ÷ 156  157 RCL C 158 x 159 RCL 9 160 ÷ 161 RCL 6 162 RCL E 163 x 164  f(i)/f'(i) 165 ÷ 166 CHS 167 GSB 5 168 RCL B 169 ÷ If value != 0, loop again 170 RND 171 X!=0? 172 GTO 6 173 RCL B Stop and display 174 RTN 175 *LBL 5 176 EEX Convert i to % and add to content of RB 177 2 178 x 179 STO + (i) 180 RTN 181 R/S
R3 +/(PMT/i) R4 [1(1+i)^{n}] R6 n(1+i)^{n1} R7 (1+i) R8 (1+i)^{n} R9 i/100 A n B i C PMT D PV E FV(BAL) I 21
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