HP12C财务计算器的使用讲义教材
财务计算器HP 12C
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退休规划解题思路
(2) 增长率g不大于5%的情况下，可以把 r-g 当作i，退休当年的生活费 当作C，并且是期初年金形式，用财务计算器进行计算。20n，2i， 0FV，12.1363 CHS PMT，g BEG，PV= 202.4148
(3)
期初增长型年金应用计算器精确计算，把
1+ 1+
2i，0PV，50FV，n=26，最早在（30+26）=56岁
退休。
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摊销—房贷中利息与本金的计算
先用PMT键算出每期本利摊还额后，运用 AMORT函数，来分出第几期中本金与利息各多 少，或是一段期间内本金与利息累计各偿还多少。
摊销功能键介绍： 按 期数 f AMORT 得到该期间支付中利息部分 按x><y得到本金部分 按RCL PV 得到贷款余额
计算未来或过去日期 例：2006年2月12日前50天是哪一日: 1. 按g M.DY键（如以前设定过则无需此步） 2. 输入2.122006 ENTER 3. 输入50 CHS，按 g DATE 显示为12,24,2005 6，表 示2005年12月24日，星期六。
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2010年7月真题
顾先生现年30岁，从现在起每年储蓄1.5万元于年 底进行投资，年投资报酬率为2%。他希望退休 时至少积累50万元用于退休后的生活，则顾先生 最早能在多少岁退休? （ ）
A．52岁
B．56岁
C．59岁
D．65岁
答案：B
解析：假设至少需要再工作n 年，1.5CHS PMT，
HP-12CP_财务计算器_使用
该菜单操作涉及五个变量，分别是期数（n），利率(i) ，现值(PV)，年金(PMT) 和终值(FV)。
如果知道其中的四个，就可以计算出另外一个。
另外，还有几个其它的重要指标需要设定：期初或期末年金(g BEG或g END)，每年复利的次数（g i），和每年付款次数(g n)。
例题1如果从第1年开始，到第10年结束，每年年末获得10,000元。
如果年利率为8%，那么，这一系列的现金流的现值和终值分别是多少？解答：1）现值：10n, 8i, 10,000PMT, 0 FV, g ENDPV=-67,100.8140（元）故现值为67,100.8140元。
2）终值：10n, 8i, 10,000PMT, 0 PV, g ENDFV=144,865.6247 (元)故终值为144,865.6247 元。
例题2李先生向银行申请20年期的购房按揭贷款100万元，合同规定利率为6.39%。
那么，李先生每月月末向银行支付的本利合计为多少？解答：20 g n, 6.39 g i, 100 PV, 0 FV, g ENDPMT= -0.7391故每月支付本利合计7391元（0.7391万元）。
例题3如果第1年年初你投资100万元，以后每年年末追加投资8.76万元，希望在第30年年末得到2,000万元。
那么，投资的收益率（必要回报率）必须是多少？解答：30n, 100 CHS PV, 8.76 CHS PMT, 2000 FV, g END,i= 8.0030故必要回报率为8.0030%（严格地讲，应该是>=8.0030%）。
例题4第1年年初投资10万元，以后每年年末追加投资5万元，如果年收益率为6%，那么，在第几年年末，可以得到100万元？解答：6 i, 10 CHS PV, 5 CHS PMT, 100 FV, g END,n= 12故在第12年年末，可得到100万元。
小王出租了一套房屋，每年租金收入2万元，年初收取。
HP12C财务计算器的使用
一元线性回归
一元线性回归：寻找两组样本X和Y之间的线性 关系，用X来解释Y。
现金流、NPV与IRR
现金流的输入
g CF0 输入期初现金流量； g CFj 输入每一期的现金流； g Nj 输入连续出现的等额现金流的次数；
（注意：输入的Nj不能超过99）
以客户角度出发判断现金流的流动方向，从而决 定现金流的正负号。
简单的统计知识介绍
均值
x1 + x2 + L+ xn 1 n x = ∑ xi = n i=1 n
例题：（AEC0002）
某客户将从第3年末开始收到一份5年期的年金，每年金额为25000元，如 果年利率为8%，那么，他的这笔年金收入的现值大约是（ ）。
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以第3-8年为年金期间，为期初年金：2.5PMT，8i，5n，0FV，g BEG，得到 PV=-10.7803，这个值是第3年年末时点上的值，再折现到当前时点： 10.7803FV，8i，3n，0PMT，g END，得到PV=-8.5578。 以第2-7年为年金期间，为期末年金：2.5PMT，8i，5n，0FV，g END，得到 PV=-9.9818，这个值是第2年年末时点上的值，再折现到当前点：9.9818FV， 8i，2n，0PMT，得到PV=-8.5578。
财务计算器运用PPT学习教案
例题2：已知每期支付、市场利率、时间， 求现值
你的客户月收入为5,000元，其中30%计划用 来缴房贷。如果银行提供的期限20年的房贷 年利率为5%，他一共可向银行贷多少钱？
20 g n
5gi 5,000 ENTER 0.3 × CHS PMT
0 FV
第22页/共40页
PV，得到227,287.9696。
其退休目标。 STO 1，储存备用。
第24页/共40页
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例题4（续）
若你的客户还有一个目标是5年后送儿子出国留学，初步估算， 需要准备40万元。那么为了实现这两个目标，他每月应定期定额 投资的总额是多少?假设现有资产完全配置在退休目标上，留学 金的准备完全靠定期定额的月储蓄。
5gn 10 g i 0 PV 40 FV PMT，得到-0.5165，（为儿子的教育支出需每年储蓄5,165元） RCL 1 +，得到-0.6284。 因此，实现两个目标，前五年的月投资额5,165+1,119=6,284元，
按题目出现的顺序输入时，没有用到的TVM功能键要输入0，才能确保把上次 输入的数据覆盖掉。或者，在输入各个变量的数据之前，按f CLEAR FIN键 清空以前的数据。
若熟悉EXCEL财务函数设置，可按照EXCEL财务函数的顺序输入：i、n、 PMT、PV、FV。
以财务计算器做货币时间价值计算时，n、i、PV、PMT、FV的输入顺序并不 会影响计算结果。
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例题1：计算 一般四则和函数运算（RPN模式）
按键：3
ENTER
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×Hale Waihona Puke 5EN（3TE4R)6 ×，+，7
(5 6)
÷，
惠普12C计算器使用指南说明书
1HP-12C Quick GuideThe Hewlett-Packard 12C (HP-12C) is HP's longest and best-selling product, in continuous production since its introduction in 1981. The HP-12C is one of only two calculators permitted on CFA Program exams (the Texas Instruments BA II Plus is the other). You may buy an HP-12C calculator for about $50 from Amazon or anotherretailer. Hewlett Packard also sells a smartphone app that mimics a full-functioning HP-12C for $14.99. Several versions of the HP-12C exist:• The Classic Gold HP-12C uses only reverse Polish notation* (RPN).• The Platinum HP-12C allows the user to choose either RPN or algebraicnotation (AN) mode. (“Normal” calculators you’re familiar with are based on AN. So, the Platinum HP-12C in AN mode might be easiest for you.• The Limited Edition 25th Anniversary HP-12C Platinum edition allows the userto choose either RPN or AN mode. HP claims it has a high-quality keyboard similar to the keyboard of the original 1980’s Classic Gold HP-12C.• The Limited Edition 30th Anniversary HP-12C edition uses only RPN. HP againclaims a high-quality keyboard.2*The "Polish" in reverse Polish notation refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in the 1920s. Polish notation is parentheses-free and the inspiration for the idea of the recursive stack, a last-in, first-out computer memory store. Studies show that RPN calculators are superior to AN calculators in terms of speed and accuracy of operation. However, as noted above, you’ll likely be up and running faster with Platinum HP-12C in the familiar AN mode.What you will need to know for the purposes of this course is summarized in this quick guide. Keep it handy as a reference as you work through problems. The extensive instruction book included with your calculator is a valuable reference for the more sophisticated functions not covered in this guide. You can also find well-done tutorials on a number of financial calculators, including the HP-12C, at:/calculator_index .Basic Functions• Turning on your calculatorThe [ON] key–or [MENU] key on some HP-12C versions–in the bottom left corner turns the calculator on or off. If you do not use thecalculator for several minutes, it will turn itself off.• Changing the displayTo change the number of decimal places displayed, key [f] then the desired number of digits. For example, [f] [2] sets the display to two decimal places past the decimal point.The default values in the calculator are ‘.’ for the decimal point and ‘,’ as the separator between groups of three digits to the left, as in 30,000.00. To reverse these, turn off the calculator, then turn it back on while holding down the [.] key.• Changing signTo change the sign of the displayed value, key [CHS].Cash inflows (i.e., money going into your wallet)are entered as positive numbers. Cash outflows3(i.e., money coming out of your wallet) are entered as negative numbers.• Mathematical calculationsThe primary difference between the HP-12C’s operation in RPN mode and AN calculators is the way operations are entered. On an AN calculator, you enter the operator between two numbers:[2] [+] [3] [=]On the HP-12C, you key:[2] [ENTER] [3] [+]The first number is entered into the “stack” memory by using [ENTER]. The second number is followed by the operator desired. Another example:Desired Calculation: What you key: What you see:(12 + 13) x 5 [1] [2] [ENTER] [1] [3] [+][5] [x]12.0025.00 125.00A bit of HP-12C terminology: The displayed value showing in the window is referred to as “x ”, i.e., the number in the “x ” register. When you key [ENTER] it moves “x ” into the “y ” register. You’ll see several keys that perform operations on “x ” and “y .” For example, the [y x ] key raises “y ” to the “x ” power. The [1/x ] key takes the inverse of “x .” Here are examples that use the [y x ] and [1/x ] keys:Desired Calculation: What you key:What you see:11065(.) [1] [.] [0] [6] [ENTER] [5] [y x ] [1/x ]1.061.34 0.7512001065(.) [1] [.] [0] [6] [ENTER][5] [y x ] [1/x ][1] [2] [0] [0] [x ] 1.06 1.34 0.75 896.714 In the examples that follow in this guide, keystrokes for numbers will be consolidated for ease of reading.• Accessing alternate functions:Many of the keys on the HP-12C perform more than one function. For example, take a closer look at the [PV] key. The [NPV] function above is accessed by first keying the gold [f] key. The [CF 0] function below is accessed by first keying the blue [g] key. For example, the sequence:[25] [g] [CF 0]enters 25 as the cash flow at time 0. The use of the [NPV] and [CF 0] keys is covered in this guide’s “Irregular Cash Flows”.• Storing numbers in memoryUp to twenty numbers may be placed into memory. The first ten ‘registers’ are accessed using the number keys [0] to [9], and thesecond ten using [.0] to [.9]. The [STO] key is for storage. Example: to enter 1.125 into the first memory slot, key[1.12] [ENTER] [5] [y x ] [STO] [0]If the display is set to two decimal places, 1.76 is displayed and also stored withoutrounding in R 0, register 0, and is available for use until the memory is cleared or another number is entered into R 0.To use the stored number in R 0, key [RCL] [0]. Example: to multiply 1000 by the 1.76 already stored in register 0, key[1000] [ENTER] [RCL] [0] [x]If the display is set to two decimal places, 1,762.34 is displayed.5• Clearing registers/memoryClear just the x register (i.e., the number that appears in the display window) by keying [CL X ]. This is useful when you make an error keying in a number.Clear the financial registers by keying [f] [FIN]. This sets all financial registers, including [n], [i], [PV], [PMT], and [FV], equal to zero. This is good form before you start any time value of money calculation.Keying [f] [REG] clears all registers, including any values stored in the x register, financial registers, and memory.6Time Value of MoneyFive keys in the upper left corner are used for many of the time value of money (TVM) calculations you’ll be introduced to in this course. [n] number of payments or time periods. [i] interest rate expressed as percent, e.g., 12% entered as [12] [i], not as [.12] [i]. [PV] present value, or value at time 0[PMT] payment, a constant amount paid or received each period. [FV] future value, specifically the value at time nGiven four of the above values, the fifth can be calculated.Example: You deposit $1,000 today into an account paying 4.00% per year. Compute the amount you will be able to withdraw in 5 years.Reminder: First, clear the financial registers by keying [f] [FIN].Data: What you key: What you see: n = 5 i = 4% PV = $1000 PMT = 0* compute FV[5] [n] [4] [i][1000] [CHS] [PV] [0] [PMT] [FV]5.004.00 -1,000.000.00 1,216.65*If [f] [FIN] is keyed to start, then the payment register would already be set to zero, so no need to key [0] [PMT].The HP-12C keeps track of cash flows moving in different directions by the using opposite signs. The $1,000 we deposit today (i.e., the present value) is entered as a negative number, and the $1,216.65 we withdraw in 5 years (i.e., the future value) is shown as a positive number. A good way to visualize how the flows are signed: If you’re taking money out of your wallet and depositing, then it’s a negative sign. If you’re withdrawing money and putting it into your wallet, then it’s a positive sign.7Example: You invest $5,000 today and $1,000 at the end of each of the next 10 years. Compute the amount you will have after 10 years if the investment earns 8% per year.Data: What you key: What you see: n = 10 i = 8 PV = $5000 PMT = $1000 calculate FV[10] [n] [8] [i][5000] [CHS] [PV] [1000] [CHS] [PMT] [FV]10.008.00 -5,000.00 -1,000.00 25,281.19• Monthly cash flowsCar loans, home mortgages, student loans, and other loans typically have monthly payments. To input the number of monthly payments when you know the number ofyears, key [g] [n]. For example, the number of payments for a 30-year mortgage can be entered as [30] [g] [n]. 360 is displayed and entered into the n register.To input the monthly interest rate when you know the annual percentage rate (APR), key [g] [i]. For example, the monthly interest rate for a mortgage with 6.00% APR, compounded monthly, can be entered as [6] [g] [i]. 0.50 is displayed and entered into the i register.Example: Compute the monthly payment on a 30-year $200,000 mortgage with a 7.5% APR, compounded monthly?Data: What you key: What you see: n = 30 x 12 i = 7.5% ÷ 12PV = $200,000FV = 0* calculate PMT[30] [g] [12x] [7.5] [g] [12÷] [200000] [PV] [0] [FV] [PMT]360.000.63200,000.000.00 -1,398.43*If [f] [FIN] is keyed to start, then the payment register would already be set to zero, so no need to key [0] [FV].8• Payments at the end of the period versus the beginning of the periodFor payments that occur at the beginning of the period, key [g] [BEG]. To confirm that the HP-12C will now make calculations presuming payments occur at the beginning of each period, “BEGIN” appears at the bottom of the display.Most of the time, though, such as when we are dealing with car loans, home mortgages, or student loans, payments occur at the end of the period. To return to the HP-12C’s default mode of presuming payments occur at the end of the period, key [g] [END]. “BEGIN” will no longer appear at the bottom of the display.• Irregular cash flowsFor calculations that involve cash flows occurring at regular intervals but with differing amounts, we enter values using [g] functions [CF 0], [CFj], and [Nj]. We can thencalculate the net present value or internal rate of return by using [f] functions [NPV] and [IRR].Enter the cash flow at time 0 by keying the value followed by [g] [CF 0]. If there is no time 0 cash flow, key [0] [g] [CF 0]. For example, if the first cash flow is -1000, key [1000] [CHS] [g] [CF 0].Enter subsequent cash flows in order using [g] [CFj]. If subsequent cash flows are different, each must be entered separately. For example, if the next two cash flows are 400 and then 500, key [400] [g] [CFj] then [500] [g] [CFj].9If equal cash flows repeat, then the number of equal cash flows can be keyed using [g] [Nj]. For example, if the next five cash flows equal 300 each, key [300] [g] [CFj] [5] [g] [Nj].Up to 20 cash flows can be stored in CF 0 to CF 19. Note that these cash flow registers are shared with the 20 memory registers. If you key [1000] [CHS] [g] [CF 0], -1000 is entered into CF 0 and will overwrite the value in the R 0 register. If you then key [400] [g] [CFj], 400 is entered into CF 1 will overwrite the value in the R 1 register.Example: Following an initial investment of $1,000, you expect cash flows of $400 in one year, $500 in two years, and $600 in three years.Data: What you key: What you see: clear all registers enter CF 0 enter CF 1 enter CF 2 enter CF 3[f] [REG] [1000] [CHS] [g] [CF 0] [400] [g] [CFj] [500] [g] [CFj] [600] [g[ [CFj]0.00-1,000.00 400.00 500.00 600.00You can now perform NPV and IRR calculations using these stored values.To calculate the NPV of the investment, you first need to enter an interest rate using the [i] key. Then key [f] [NPV].Calculation of internal rate of return requires no additional information. Key [f] [IRR].10Example: Continuing the example from above, if the cost of capital is 14.5% per year, what is the NPV and IRR?Data: What you key: What you see:enter interest rate calculate NPV calculate IRR [14.5] [i] [f] [NPV] [f] [IRR] 14.50 130.43 21.65。
财务计算器的使用
财务计算器的运用原则-3
• 在解决货币时间价值问题时 ，最好先画出现金流量与时间 图。
• 把理财目标当作基准点 ，基准点之前我们通过累积资产来 实现理财目标 ，是用现值（比如现有资产）或年金（比如 每期储蓄）来求复利终值或年金终值。
• 基准点之后可以理解为先借贷来实现理财目标 ，之后再分期摊还， 是用终值（比如预留遗产额）或年金（比如每期学费、每期生活 费、每期房贷）来求复利现值或年金现值。
• 假设他向银行贷23万元 ，并将还款上限提高至收入的
• 40%，则几年可以还清贷款?
•
g END
• 5gi
• 230000 PV
•
5000 ENTER 0.4 × CHS PMT
• 0 FV
•n • 12 ÷ , 得到13.0833。
• 因此 ， 14年后可以还清（实际上需要13年零1个月就
• 可以还清）
第七页 ，本课件共46页
小数位数的设置
• 小数位数的设置 :不设置时初始值为两位小数 ，更改设 置时 ，如要改为四位小数 ，按f 4即可。
• 考试时最好设为4位小数，输入PV或FV时可以 • 万元计，得出PMT时小数点4位，答案可以精
• 确到元。
• 小数位数设置将保持有效 ，不会因退出或重新开机 而改变 ，要重新设置才会改变。
• 如果前段现值与年金所累计的资产 ，等于后段终值与年金所 算出的负债之时 ，就是理财目标可以实现的时间点 。而折现 率的高低 ， 则是决定何时资产会等于负债的关键因素。
第十一页 ，本课件共46页
付款和复利计算设置
• 计算每月付款额PMT时，就按g i和g n， • 计算每年付款额PMT时 ，就按i和n， • 计算其他期限付款额PMT时，相应输PMT和
2-02财务计算器运用HP12C培训资料
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例题4（续）
若你的客户还有一个目标是5年后送儿子出国留学，初步估算，需 要准备40万元。那么为了实现这两个目标，他每月应定期定额投 资的总额是多少?假设现有资产完全配置在退休目标上，留学金的 准备完全靠定期定额的月储蓄。
5gn 10 g i 0 PV 40 FV PMT，得到-0.5165，（为儿子的教育支出需每年储蓄5,165元） RCL 1 +，得到-0.6284。 因此，实现两个目标，前五年的月投资额5,165+1,119=6,284元，
在解决货币时间价值问题时，最好先画出现金流量时间 图。
把理财目标当作基准点，基准点之前我们通过累积资产 来实现理财目标，是用现值（比如现有资产）或年金（ 比如每期储蓄）来求复利终值或年金终值。
基准点之后可以理解为先借贷来实现理财目标，之后再 分期摊还，是用终值（比如预留遗产额）或年金（比如 每期学费、每期生活费、每期房贷）来求复利现值或年 金现值。
投资期间（比如贷款期间）
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每期金额
期初年金与期末年金的设置
系统默认设置为期末年金。 期初年金模式：按g再按BEG，此时计算器的
显示屏上会出现小字显示的BEGIN。 按g再按END，显示屏上的BEGIN会消失，计算
器又恢复到期末年金的模式。 在理财规划方面，生活费、房租与保险费通
常假设发生在期初。收入的取得、每期房贷 本息的支出、利用储蓄来投资等等，通常都 假设发生在期末。若试题中特别注明发生在 期初或期末，则以试题中注明的条件为准。
7% 1.070 1.145 1.225 1.311 1.403 1.501 1.606 1.718 1.838 1.967 2.105 2.252 2.410 2.579 2.759