HP 35s User Manual

							 
 
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HP 35s Bond Prices 
 
 
 
 
Bond Prices 
 
The Time Value of Money on the HP 35s 
 
Practice solving for the price of a bond 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s Bond Prices 
 
hp calculators - 2 - HP 35s Bond Prices - Version 1.0 
Bond Prices 
 
A bond is a financial instrument where a company, government entity, or individual borrow money with the promise to 
pay interest periodically and to repay the initial amount borrowed at a specified future date. Bonds will usually have a 
specified interest rate (called the coupon rate) and are most often in denominations of $1,000. Bonds also usually pay 
interest every six months. The interest rate the bond pays is fixed when the bond is first sold or issued, but changes in 
the market interest rate will change the price of the bond over its lifetime. If market interest rates have gone up since the 
bond was purchased, the price of the bond will have gone down. If, however, market interest rates have gone down 
since the bond was purchased, the price of the bond will have gone up. The HP 35s  can directly solve for bond prices 
using the time value of money formula below in simple situations where a bond interest payment is exactly one period 
away. For other situations, the answers will be approximations. 
 
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.   
						

							 
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HP 35s Bond Prices 
 
hp calculators - 3 - HP 35s Bond Prices - Version 1.0 
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 :. 
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 bond prices. 
 
Practice solving for the price of a bond 
 
Example 1: A bond with 20 years left has a 5% coupon rate and pays interest semiannually. If the market interest 
 rate is now 6%, compounded semiannually, for what price should this bond be selling? 
 
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:-
 
-561 
 
 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 
 
-The payment is found by multiplying the coupon interest rate, 5%, by the face value of the bond, $1,000,  
 then dividing the result by 2 for the semiannual interest payment amount, $25. 
 
-In RPN mode, press: ;&
						

							 
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HP 35s Bond Prices 
 
hp calculators - 4 - HP 35s Bond Prices - Version 1.0 
 
-In RPN mode, press: >2=*: 
 In algebraic mode, press: >*=2:-
 
 Figure 3 
 
-In RPN mode, press: =&2=$: 
 In algebraic mode, press: =&$=2:-
 
 Figure 4 
 
-In either RPN or algebraic mode, press: %&&&: 
  
 Figure 5 
 
Answer: The price of the bond is $884.43. 
 
Example 2: A bond with 10 years left until it matures has a 6% coupon rate and pays interest semiannually. What is the  
 price of this bond, if the market interest rate is 5%, compounded semiannually? 
 
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:-
 
-561 
 
 The HP 35s SOLVER displays the first variable encountered in the equation as it begins its solution.  
 The displays shown in the figures below assume the preceding example has just been worked. Follow  
 the keystrokes shown below and the solution should be found as described. 
 
 Figure 6 
 
-The payment is found by multiplying the coupon interest rate, 6%, by the face value of the bond, $1,000,  
 then dividing the result by 2 for the semiannual interest payment amount.   
						

							 
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HP 35s Bond Prices 
 
hp calculators - 5 - HP 35s Bond Prices - Version 1.0 
-In RPN mode, press: ;&>2%&&&$=*: 
 In algebraic mode, press: ;&>$%&&&*=2:-
 
 Figure 7 
 
-In RPN mode, press: 
						

							 
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HP 35s Bond Prices 
 
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 In RPN mode, press: ;&
						

							 
 
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HP 35s  Trend Lines 
 
 
 
 
Trend Lines 
 
Practice predicting the future using trend lines 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Trend Lines 
 
hp calculators - 2 - HP 35s  Trend Lines - Version 1.0 
Trend Lines  
A trend line is actually an equation of a line in the form Y = mX + b, where m is the slope of the line and b is the Y-
intercept. Linear regression calculates the equation for this line by minimizing the sum of the squared residuals between 
the actual data points and the predicted data points using the estimated line’s slope and intercept. Once the slope and 
intercept have been calculated, it is fairly easy to substitute other values for X and predict a corresponding value for Y, or 
to substitute a value for Y and predict a value for X. When the X value is a measure of time (months or years, for 
example), the equation is specifically referred to as a trend line. These are often used to predict future sales growth 
given past sales data. Be aware, however, that it is rarely a good idea to use such an equation to predict too far into the 
future from the actual data used, since circumstances can change rather quickly. Also be aware that these predictions 
are linear in nature and make no adjustment for any seasonality that may exist. 
 
On the HP 35s, values are entered into the statistical / summation registers by keying in the number (or pair of numbers) 
desired and pressing !. This process is repeated for all numbers or pair of numbers.  When entering a pair of 
numbers in RPN or algebraic mode, key the Y value, press , then key the X value and press !.  
 
To view the linear regression results, press #$. The HP 35s displays a menu of relevant values. Items on this 
menu are viewed by pressing the % or & cursor keys of the HP 35s. 
 
This menu allows you to predict a value for X given a Y value, or predict a value for Y given an X value. It also displays 
the linear regression lines correlation, slope, and y-intercept. The correlation will always be between –1 and +1, where 
values closer to –1 and +1 indicating a good “fit” of the line to the data. Values nearer to zero indicate little to no “fit.” 
Little reliance should be placed upon predictions made where the correlation is not near –1 or +1. Exactly how far away 
from these values the correlation can be and the equation still be considered a good predictor is a matter of debate. To 
use a value displayed on the menu, press the  button and the value will be copied for further use. This is 
illustrated in the problems below.  
Practice predicting the future using trend lines  
Example 1: John’s store has had sales for the last 5 months of $150, $165, $160, $175, and $170. Use a trend line to  
 predict sales for months 6 and 7 and also predict when estimated sales would reach $200. What is the  
 correlation of the regression line? 
 
Solution: Be sure to clear the statistics / summation memories before starting the problem.  
 ()*
 
 In RPN or algebraic mode, press: 
 
 +,-+!+.,/!+.-0!*
*+1,)!+1-,! 
  
 To view the linear regression results, press #$. Figure 2 displays the menu shown. 
 
 Figure 2 
 
 In either RPN or algebraic mode, press: && to view the correlation.   
						

							 
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HP 35s  Trend Lines 
 
hp calculators - 3 - HP 35s  Trend Lines - Version 1.0 
 Figure 3 
 
 In either RPN or algebraic mode, press: & to view the slope of the linear regression / trend line. 
 
 Figure 4 
  
 In either RPN or algebraic mode, press & to view the y-intercept of the linear regression / trend line. 
 
 Figure 5 
 
 To estimate sales for month 6, do the following: In either RPN or algebraic mode, press:
 2.#$& 
 
 Figure 6 
 
 To estimate sales for month 7, do the following: In either RPN or algebraic mode, press:
 21#$& 
 
 Figure 7 
 
 To estimate the month during which sales would reach $200, do the following: In either RPN or algebraic 
mode, press: 2/--#$ 
 
 Figure 8 
 
Answer: Sales in month 6 are predicted to be $179 and in month 7 $184. Sales are predicted to reach $200  
 between months 10 and 11. The correlation is 0.82, which indicates a fairly strong relationship and  
 predictive ability.   
						

							 
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HP 35s  Trend Lines 
 
hp calculators - 4 - HP 35s  Trend Lines - Version 1.0 
Example 2: A store’s quarterly sales for the last 2 years have been $30,000, $31,200, $30,500, $32,400, $32,200,  
 $33,100, $32,600 and $33,250. Use a trend line to predict sales for the next year and also predict when  
 estimated sales would reach $38,000. What is the correlation of the linear regression line? 
 
Solution: The X values will be the quarters of 1 through 8. The Y values will be the existing sales numbers.  
 Predictions will be made for quarters 9, 10, 11, and 12.  Be sure to clear the statistics / summation  
 memories before starting the problem.  
 ()*
 
 In RPN or algebraic mode, press: 
 
 0----+!0+/--/!*
*0-,--0!0/)--)! 
 0//--,!00+--.!*
*0/.--1!00/,-3! 
  
 To view the linear regression results, press #$. Figure 9 displays the menu shown. 
 
 Figure 9 
 
 In either RPN or algebraic mode, press: && to view the correlation. 
 
 Figure 10 
 
 In either RPN or algebraic mode, press: & to view the slope of the linear regression / trend line. 
 
 Figure 11 
  
 In either RPN or algebraic mode, press & to view the y-intercept of the linear regression / trend line. 
 
 Figure 12 
 
 To estimate sales for the first quarter of the next year (quarter 9), do the following:  
 
 In either RPN or algebraic mode, press: 24#$&