HP 35s User Manual

							 
hp calculators 
 
HP 35s  Percentages and Percentage Changes 
 
hp calculators - 3 - HP 35s  Percentages and Percentage Changes - Version 1.0 
Example 2: What is 12% added to $1,235.17? 
 
Solution: In RPN mode, the calculation shown in Figure 1 has left the original number in register Y, and 12% of it in 
register X. Pressing - adds the 12 percent to the original number, giving the answer. 
 
 Figure 3 
 
 In algebraic mode, press: 
 
 #$()#*-+&#$()#*/#$% 
 
 
 Figure 4 
 
 Note that in algebraic mode “n” percent added to something is obtained by adding the percentage to the 
original value. 
 
Answer: 12% added to $1,235.17 is $1,383.39 to the nearest cent. 
 
Example 3: The local grocery store is offering 8% off all tinned foods this week. What will be the cost of buying 5 tins 
that normally cost $1.85 each? 
 
Solution: In RPN mode, the usual cost of 5 tins is first calculated by multiplying 1.85 by 5. Then 8% is calculated as 
in Example 1. Finally, the 0 key is used to subtract the percentage from the original. 
 
 #)1(%(.1+&0,
 
 Figure 5 
 
 In algebraic mode, the price of 5 tins is also calculated first, then the percent discount is computed 
 
 #)1(.(%,
,
 Figure 6 
,
,+20+&+2/1% 
 
 Figure 7   
						

							 
hp calculators 
 
HP 35s  Percentages and Percentage Changes 
 
hp calculators - 4 - HP 35s  Percentages and Percentage Changes - Version 1.0 
Answer: 8% subtracted from 5 times $1.85 gives a price of $8.51 for the 5 tins, to the nearest cent. 
 
Practice working problems involving percentage changes 
 
The examples so far have shown how percentages are calculated, and how they are added or subtracted, by use of the 
& key. Calculating a percent change is carried out using 3 above the 4 key. 
 
Example 5: An investor began the day with $28,758.91 as the value of her investment only to find that when the market 
closes in the afternoon, the investment is worth $28,701. By how much did the market change during the 
day? 
 
Solution: In RPN mode, enter the old value, the new value, and then the 3 key is pressed.  
 
 $1*(1)5#%$1*6#!3 
 
 Figure 8 
 
 As with the & key, the original value stays in register Y so that it can be used again. 
 
 In algebraic mode, press: 
 
 !3$1*(1)5#/$1*6#% 
 
 Figure 9 
 
Answer: The market changed by -0.20 during the day, in other words it fell by 0.2%. 
 
Note: It is important to remember that the change is calculated as a percentage of the first number. If you have 100 
apples and give 20 to your neighbor, then you have 80 apples left and the percentage change is -20/100 or -20%. If you 
have 80 apples and your neighbor gives you 20 then you have 100 again, but this time the change is 20/80 or +25%. 
This means that a percent change down, followed by exactly the same percent change up, does not bring you back to 
the original number. 
 
Finally, if FIX 2 mode was set before these practice problems were done, it may be useful to set a different mode now 
they are finished. 
 
Press:,!7 to set “All” mode.   
						

							 
 
hp calculators 
 
 
 
 
HP 35s House Payment Calculations 
 
 
 
 
House payments 
 
The Time Value of Money on the HP 35s 
 
Practice solving house payment calculation problems 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
hp calculators 
 
HP 35s House Payment Calculations 
 
hp calculators - 2 - HP 35s House Payment Calculations - Version 1.0 
House payments 
 
The payment required to pay off a house over time involves the solution of an ordinary annuity with the value of the 
payment as the unknown variable. 
 
The Time Value of Money on the HP 35s 
 
To solve time value of money problems on the HP 35s, the formula below is entered into the flexible equation solver built 
into the calculator. This equation expresses the standard relationship between the variables in the time value of money 
formula. The formula uses these variables: N is the number of compounding periods; I is the periodic interest rate as a 
percentage (for example, if the annual interest rate is 15% and there are 12 payments per year, the periodic interest 
rate, i, is 15÷12=1.25%); B is the initial balance of loan or savings account; P is the periodic payment; F is the future 
value of a savings account or balance of a loan. 
 
Equation: P x 100 x ( 1 - ( 1 + I ! 100 )^ -N)  ! I + F x ( 1 + I ! 100 ) ^ -N + B 
 
To enter this equation into the calculator, press the following keys on the HP 35s: 
 
!#$%&&$4%4%()*%&&+,-
./+*)(0$4%()*%&&+,.-
/(12 
 
To verify proper entry of the equation, press 
 
34 
 
and hold down the 4-key. This will display the equation’s checksum and length. The values displayed should be a 
checksum of CEFA and a length of 41. 
 
To solve for the different variables within this equation, the 56 button is used. This key is the right shift of the 
! key. 
 
Notes for using the SOLVE function with this equation: 
 
1) If your first calculation using this formula is to solve for the interest rate I, press %57)-before beginning. 
2) Press !. If the time value of money equation is not at the top of the list, press 8or 9 to scroll through the 
list until the equation is displayed. 
3) Determine the variable for which you wish to solve and press: 
a) 56/ to calculate the number of compounding periods. 
b) 56) to calculate the periodic interest rate. Note: this will need to be multiplied by the number of 
compounding periods per year to get the annual rate. If the compounding is monthly, multiply by 12. 
c) 561 to calculate the initial balance (or Present Value) of a loan or savings account. 
d) 56# to calculate the periodic payment. 
e) 560 to calculate the future value of a loan or savings account. 
4) When prompted, enter a value for each of the variables in the equation as you are prompted and press :. The 
solver will display the variables’ existing value. If this is to be kept, do not enter any value but press : to 
continue. If the value is to be changed, enter the changed value and press :. If a variable had a value in a 
previous calculation but is not involved in this calculation (as might happen to the variable P (payment) when solving 
a compound interest problem right after solving an annuity problem), enter a zero for the value and press :.   
						

							 
hp calculators 
 
HP 35s House Payment Calculations 
 
hp calculators - 3 - HP 35s House Payment Calculations - Version 1.0 
5) After you press : for the last time, the value of the unknown variable will be calculated and displayed. 
6) To do another calculation with the same or changed values, go back to step 2 above. 
 
The SOLVE feature will work effectively without any initial guesses being supplied for the unknown variable with the 
exception noted above about the variable I in this equation. This equation follows the standard convention that money in 
is considered positive and money out is negative. 
 
The practice problems below illustrate using this equation to solve a variety of problems involving house payment 
calculations. 
 
Practice solving house payment calculation problems 
 
Example 1: Jill bought a house for $210,000. Her 30-year loan will have an interest rate of 6%, compounded monthly.  
 What is the size of her monthly house payment? 
 
Solution: First, enter the time value of money equation into the HP 35s solver as described earlier in this document.  
 
 Then press !-and press 8or 9 to scroll through the equation list until the time value  
 of money equation is displayed. Then press:-
 
-56# 
 
 The HP 35s SOLVER displays the first variable encountered in the equation as it begins its solution.  
 The value of 0.0000 is displayed below if this is the first time the time value of money equation has been  
 solved on the HP 35s calculator. If any previous equations have used a variable used in the time value of  
 money equation, they may already have been assigned a value that would be displayed on your HP 35s  
 display. Follow the keystrokes shown below and the solution should be found as described. 
 
 Figure 1 
 
-In RPN mode, press: ;2%
						

							 
hp calculators 
 
HP 35s House Payment Calculations 
 
hp calculators - 4 - HP 35s House Payment Calculations - Version 1.0 
-In either RPN or algebraic mode, press: &: 
 
 Figure 4 
 
-In either RPN or algebraic mode, press: 2%2%&&&.:-(Enters B) 
 
 In algebraic mode, press: >*%$%&&&.:-(Enters B)  
 Figure 6 
 
Answer: $1,304.81 (Note that the loan amount was entered as a negative number)  
 
Example 3: Jeff bought a house for $125,000 and financed it with a 20-year loan at a rate of 5.25%, compounded 
 monthly. What is the size of Jeff’s monthly house payment?   
						

							 
hp calculators 
 
HP 35s House Payment Calculations 
 
hp calculators - 5 - HP 35s House Payment Calculations - Version 1.0 
 
Solution: First, enter the time value of money equation into the HP 35s solver as described earlier in this document.  
 
 Then press !-and press 8or 9 to scroll through the equation list until the time value  
 of money equation is displayed. Then press:-
 
-56# 
 
 The HP 35s SOLVER displays the first variable encountered in the equation as it begins its solution.  
 These displays are not shown in the rest of this example. Follow the keystrokes shown below and the  
 solution should be found as described. 
 
 In RPN mode, press: >?2%
						

							 
 
hp calculators 
 
 
 
 
HP 35s Property Appreciation 
 
 
 
 
Property Appreciation 
 
The Time Value of Money on the HP 35s 
 
Practice solving property appreciation problems 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
hp calculators 
 
HP 35s Property Appreciation 
 
hp calculators - 2 - HP 35s Property Appreciation - Version 1.0 
Property Appreciation 
 
When the value of a piece of property increases over time, it has appreciated in value. If a value in the past is known, it 
is possible to solve the resulting compound interest problem to determine the rate of this appreciation. 
 
The Time Value of Money on the HP 35s 
 
To solve time value of money problems on the HP 35s, the formula below is entered into the flexible equation solver built 
into the calculator. This equation expresses the standard relationship between the variables in the time value of money 
formula. The formula uses these variables: N is the number of compounding periods; I is the periodic interest rate as a 
percentage (for example, if the annual interest rate is 15% and there are 12 payments per year, the periodic interest 
rate, i, is 15÷12=1.25%); B is the initial balance of loan or savings account; P is the periodic payment; F is the future 
value of a savings account or balance of a loan. 
 
Equation: P x 100 x ( 1 - ( 1 + I ! 100 )^ -N)  ! I + F x ( 1 + I ! 100 ) ^ -N + B 
 
To enter this equation into the calculator, press the following keys on the HP 35s: 
 
!#$%&&$4%4%()*%&&+,-
./+*)(0$4%()*%&&+,.-
/(12 
 
To verify proper entry of the equation, press 
 
34 
 
and hold down the 4-key. This will display the equation’s checksum and length. The values displayed should be a 
checksum of CEFA and a length of 41. 
 
To solve for the different variables within this equation, the 56 button is used. This key is the right shift of the 
! key. 
 
Notes for using the SOLVE function with this equation: 
 
1) If your first calculation using this formula is to solve for the interest rate I, press %57)-before beginning. 
2) Press !. If the time value of money equation is not at the top of the list, press 8or 9 to scroll through the 
list until the equation is displayed. 
3) Determine the variable for which you wish to solve and press: 
a) 56/ to calculate the number of compounding periods. 
b) 56) to calculate the periodic interest rate. Note: this will need to be multiplied by the number of 
compounding periods per year to get the annual rate. If the compounding is monthly, multiply by 12. 
c) 561 to calculate the initial balance (or Present Value) of a loan or savings account. 
d) 56# to calculate the periodic payment. 
e) 560 to calculate the future value of a loan or savings account. 
4) When prompted, enter a value for each of the variables in the equation as you are prompted and press :. The 
solver will display the variables’ existing value. If this is to be kept, do not enter any value but press : to 
continue. If the value is to be changed, enter the changed value and press :. If a variable had a value in a 
previous calculation but is not involved in this calculation (as might happen to the variable P (payment) when solving 
a compound interest problem right after solving an annuity problem), enter a zero for the value and press :.