HP 12c Owners Manual
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Section 15: Savings 161 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 161 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm REGISTERS n: # Periods. i: Nom. Rate/n PV: 0 PMT: Used. FV: Eff. Rate R0–R.9: Unused 1. Key in the program. 2. Key in the annual nominal rate as a percentage then press \. 3. Key in the number of compounding periods per year then press t to obtain the effective annual interest rate. 4. For a new case return to step 2. Example 2: What is the effective annual rate of interest if the annual nominal rate of 5 1/4% is compounded monthly? Keystrokes Display 5.25\ 12t 5.38 Percent effective interest rate. Effective Rate Converted to Nominal Rate Given an effective interest rate and the number of compounding periods per year, this routine calculates the nominal interest rate. 1. Press fCLEARG. 2. Key in the number of periods per year then press n. 3. Key in 100 then press \$. 4. Key in the effective annual rate as a percentage then press +ÞM¼. 5. Press :n§ to obtain the annual nominal rate. Example: Find the nominal rate if the effective annual rate is 5.35% compounded quarterly. Keystrokes Display fCLEARG 4n100\$ 100.00 5.35+Þ –105.35 M¼ 1.31 :n§ 5.25 Percent nominal interest rate.
162 Section 15: Savings File name: hp 12c_users guide_English_HDPMBF12E44 Page: 162 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Nominal Rate Converted to Continuous Effective Rate This procedure converts a nominal annual interest rate to the continuous effective rate. 1. Press 1\. 2. Key in the nominal rate as a percentage then press b. 3. Press g>à. Example: What is the effective rate resulting from a 5 1/4% passbook rate with continuous compounding? Keystrokes Display 1\5.25b g> 1.05 à 5.39 Continuous rate.
163 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 163 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Section 16 Bonds 30/360 Day Basis Bonds A bond is a contract to pay interest, usually semiannually, at a given rate (coupon) and to pay the principal of the bond at some specified future date. A bond which is calculated on a 30/360 day basis is one in which the day count basis is computed using 30 days in a month and 360 days in a year. The following program solves for the price given the yield or for the yield given the price of a semiannual coupon bond which is calculated on a 30/360 day basis and is held for more than six months. KEYSTROKES DISPLAY KEYSTROKES DISPLAY fs :6 24- 45 6 fCLEARÎ 00- § 25- 20 fCLEARG 01- 42 34:0 26- 45 0 g× 02- 43 7gm 27- 43 35 :2 03- 45 2gi39 28-43, 33 39 2 04- 22 29- 2 z 05- 10z 30- 10 P 06- 14¼ 31- 12 ?6 07- 44 6$ 32- 13 :5 08- 45 5Þ 33- 16 + 09- 40~ 34- 34 M 10- 15- 35- 30 :3 11- 45 3gF 36- 43 36 :4 12- 45 4~ 37- 34 gÒ 13- 43 26gi00 38-43, 33 00
164 Section 16: Bonds
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KEYSTROKES DISPLAY KEYSTROKES DISPLAY
d 14- 33d 39- 33
1 15- 1:1 40- 45 1
8 16- 8+ 41- 40
0 17- 0Þ 42- 16
z 18- 10$ 43- 13
n 19- 11¼ 44- 12
gT 20- 43 242 45- 2
1 21- 1§ 46- 20
~ 22- 34fs
- 23- 30
REGISTERS
n:
∆ days/180 i: Yield/2 PV: Price PMT: Coupon/2.
FV: Red+Cpn./2
R0: Yield R1: Price. R2: Coupon
R3: Dset R4: Dmat R5: Redemption R6: Coupon/2.
R7–R.3: Unused
1. Key in the program.
2. If the C status indicator is not displayed, press ?É.
3. Key in the annual coupon interest rate as a percentage then press ?2.
4. Key in the settlement date (MM.DDYYYY)
* then press ?3.
5. Key in the maturity date (MM.DDYYYY)* then press ?4.
6. Key in the redemption value as a percentage of par then press ?5.
7. If price is desired:
a. Key in the desired yield to maturity as a percentage then press ?0.
b. Press t to calculate price as a percentage of par value.
c. Press ~ to display accrued interest due the seller.
* For information about date format see pages 29 to 30.
Section 16: Bonds 165 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 165 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. 8. If yield is desired: a. Press 0?0. b. Key in the price as a percentage of par value and press ?1. c. Press t to compute annual yield to maturity. For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. Example 1: What price should you pay on August 28, 2004 for a 5 1/2% bond (computed with a 30/360 basis) that matures on June 1, 2008, if you want a yield of 7 3/4%? What price should you pay for a yield of 8%? This problem assumes a redemption value of 100. Keystrokes Display ?Æ Set compound interest mode if the C indicator is not on. 5.5?2 5.50 Coupon into register 2. 8.282004?3 8.28 Settlement date into register 3. 6.012008?4 6.01 Maturity date into register 4. 100?5 100.00 Redemption value into register 5. 7.75?0 7.75 Yield into register 0. t 92.77 Price (calculated). ~ 1.33 Accrued interest (calculated). 8?0 8.00 New yield into register 0. t 92.01 Price to yield 8% (calculated). ~ 1.33 Accrued interest (calculated). + 93.34 Total price paid. Example 2: The market is quoting 93 3/8% for the bond described in example 1. What yield will that provide? What would be the yield to maturity if 92% were the quoted price? Keystrokes Display 93.34 From previous example. 0?0 3\8z 93+?1t 7.55 Yield at 933/8% (calculated). 92?1t 8.00 Yield at 92% (calculated).
166 Section 16: Bonds File name: hp 12c_users guide_English_HDPMBF12E44 Page: 166 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Annual Coupon Bonds For bonds which have annual coupons, use the following hp 12c program to evaluate price and accrued interest on an Actual/Actual day basis. This program may be modified for annual coupon bonds to be calculated on a 30/360 day basis. KEYSTROKES DISPLAY KEYSTROKES DISPLAY fs gÒ 19- 43 26 fCLEARÎ 00- ?7 20- 44 7 fCLEARG 01- 42 34:6 21- 45 6 g 02- 43 8:4 22- 45 4 :0 03- 45 0gÒ 23- 43 26 n 04- 11:7 24- 45 7 :2 05- 45 2z 25- 10 P 06- 14n 26- 11 :1 07- 45 10 27- 0 ¼ 08- 12P 28- 14 :3 09- 45 3M 29- 15 M 10- 15Þ 30- 16 $ 11- 13:n 31- 45 11 :5 12- 45 5:2 32- 45 2 Æ 13- 26Þ 33- 16 6 14- 6§ 34- 20 Þ 15- 16t 35- 31 - 16- 30- 36- 30 ?6 17- 44 6fs :5 18- 45 5
Section 16: Bonds 167
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REGISTERS
n: Used i: Yield PV: Used PMT: Cpn. or 0
FV: Used
R0: # Periods (n) R1: Yield R2: Coupon
R3: Redemption R4: Settlement R5: Next Cpn. R6: Last Coupon
R7: Used R8–R.5: Unused
For annual coupon bonds calculated on a 30/360 day basis, insert d
after
gÒ
at steps 19 and 23 (making the program two steps longer).
1. Key in the program and press ?É if the C status indicator is not
displayed.
2. Key in the total number of coupons which are received and press ?0.
3. Key in the annual yield as a percentage then press ?1.
4. Key in the amount of the annual coupon then press ?2.
*
5. Key in the redemption value then press ?3.
*
6. Key in the settlement (purchase) date
† then press ?4.
7. Key in the date of the next coupon then press ?5.
8. Press t to obtain the amount of accrued interest.
9. Press t to determine the priceof the bond.
10. For a new case, return to step 2.
Example:
What is the price and accrued interest of a 20-year Eurobond with
annual coupons of 6.5% purchased on August 15, 2004 to yield 7%. The next
coupon is received on December 1, 2004.
Keystrokes Display
?Æ
Set compound interest mode if the C
indicator is not on.
20?0
20.00 Total number of coupons.
7?1
7.00 Annual yield.
6.5?2
6.50 Annual coupon rate.
100?3
100.00 Redemption value.
8.152004?4
8.15 Settlement date.
12.012004?5
12.01 Next coupon date.
t
–4.58 Accrued interest.
t
–94.75 Purchase price.
* Positive for cash received; negative for cash paid out.
† For information about date format see pages 29 to 30.
File name: hp 12c_users guide_English_HDPMBF12E44 Page: 169 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Appendixes
170 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 170 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Appendix A The Automatic Memory Stack Four special registers in the hp 12c are used for storing numbers durin g calculations. To understand how these re gisters are used, they should be visualized as stacked on top of each other. (For this reason, they are generally referred to as the “stack registers” or collectively as “the stack.”) The stack registers are designated X, Y, Z, and T. Unless the calculator is in Program mode, the number shown in the display is the number in the X-register (modified according to the current display format). The number in the X-register — and, for two-number functions, the number in the Y-register — are the number(s) used in calculations. The Z- and T-registers are used primarily for the automatic retention of intermediate results during chain calculations, as described in section 1. Before we discuss the details of the stack operation, let’s take a quick look at how the stack is used in a simple arithmetic calculation and in a chain calculation. For each key pressed in the keystroke sequence, the diagram illustrating the calculation shows, above the key, the numbers in each of the stack registers after that key is pressed. First, let’s consider the calculation of 5 – 2: The diagram shows why we said in section 1 that the \ key separates the second number entered from the first number entered. Note also that this positions the 5 in the Y-register above the 2 in the X-register — just like they would be positioned if you wrote the calculation vertically on paper: