Savings Plan – Regular Contribution With Interest
储蓄计划 – 定期连利存款
Investments grow overtime as interest builds. Although making safe investments for your future is a good idea, making a few investments and waiting for them to grow is not enough. To plan for your future you will need to regularly contribute money to a Savings Plan. These are also know as and RSP Retirement Savings Plan.
投资会随着利息的增长也会不断增长。尽管安全投资是个很好的选择，但是仅仅只是投资然后坐等他们增值还是远远不够的。要为你的未来做个好的计划的话，你得做好你的储蓄计划，也就是所谓的RSP退休储蓄计划。
Although you might think you are too young to think about retirement now, saving enough money to retire is a long and difficult task. The choices you make now will effect you for the rest of your life. Start saving early.
也许你在想这么年轻就考虑退休后的事情是否为时过早，但是为退休做好足够的储蓄还是一件长期且艰巨的任务。你现在做的种种决定都会对你的未来产生重大影响。所以从现在就开始行动吧。
Think back to your Savings Target that included the increase in living cost because of Inflation. How long do you think it will take you to save enough money to make you target? How much money would you have to regularly contribute to save enough money to retire? How much can you afford to contribute every month?
回想一下上次做的关于通货膨胀导致居民生活消费增长的储蓄目标设计，若想达到你的目标，你需要多长时间完成足够的储蓄金额？还要从现在开始你要定期存入多少金额？每个月你能存入多少？
Creating the formula 创建公式
Abbreviations used for the formulas in this section
在本公式中用到的术语缩写形式
- A = Accumulated Total 累计总和
- P = Initial Principle 本金
- c = Contributions (equal annual contributions) 存款
- r = Rate (Interest Rate) 利率
- n = Number of years 年数
To keep the math simple for this example we will create a formula based on yearly interest and regular contributions. However This formula could be expanded to factor in compound interest for more advanced calculations.
为使计算更简单一些，在年利率和定期存款的基础上创建了一个公式，当然对于更为复杂的计算该公式也可以扩展。
Each Savings Plan will start with an initial investment. Each year this investment will receive interest. This section of the formula is “Initial Principle” multiplied by the formula for interest.
每一个储蓄存款都是以初始投资开始的。每一年该投资都会获得一笔利息。该公式就是本金乘以利息公式后的金额。
A = P(1+r)n
Regular contributions will also be made in addition to the Initial Principle invested. These regular contributions will also receive interest. Regular yearly contributions create a pattern though. In math this is called a Geometric Series. Any Geometric Series can be simplified. However it is important to understand how the series works. By simplifying a Geometric Series we can quickly calculate a total for any year in the future. Irregular contributions are much more difficult to calculate, and require you to understand how the series works.
除了投资本金之外也要进行定期存款。这些存款都会有一笔利息，而每年都会往上增加，在数学上叫做等比数列。任何等比数列都可以简化，但是理解每一个等比数列还是很重要的。通过简化等比数列我们可以很快地计算出未来任何一年的总额。而不定期存款计算起来就麻烦多了，且你要吃透等比数列的含义。
| Year 年 | Process in building the formula. 创建等比数列公式过程。 |
|---|---|
| 1 | P(1+r) + c(1+r) |
| 2 | P(1+r)2 + c{ (1+r) + (1+r)2 } |
| 3 | P(1+r)3 + c{ (1+r) + (1+r)2 + (1+r)3} |
| 4 | P(1+r)4+ c{ (1+r) + (1+r)2 + (1+r)3 + (1+r)4} |
| 5 | P(1+r)5 + c{ (1+r) + (1+r)2 + (1+r)3 + (1+r)4 + (1+r)5} |
| n | P(1+r)n + c{ (1+r) + (1+r)2 + (1+r)3 + (1+r)4 + (1+r)5 + ….. + (1+r)n} |
When we simplify the formula we reduce the Geometric Series created by the regular contributions and the interest to its simplest form. We are then left with the formula:
当我们简化公式时，我们将定期存款和利息简化到最简短的形式，最后得到这样的公式：
A = P(1 + r)n + c [ {(1 + r)n – 1} / r ]
The formula looks very large when written out, but it can be simplified into smaller sections. You could also look at this formula as the following two concepts.
看起来这个公式非常的庞大，但是可以划分为几个小的部分。参照以下两个概念再次看一下这个公式。
A = “Initial Principle with Interest” + “Regular Contributions with Interest”
A = “ 连利本金” + “连利定期存款”
We have created a simple formula that will calculate our accumulated total based on yearly interest and regular yearly contributions. This will allow us to make basic calculations. Professional Financial Planners will need to create even more complex formulas to factor in compound interest, irregular monthly contributions, and even make compensations for inflation.
这样我们就创建了一个简单的公式来计算包括年利率和定期存款的总金额了。我们可以用该公式做基本的计算了。而专业的金融家们却要创建更为复杂的公式来计算包括复利、不定期存款以及由于通货膨胀导致的赔偿金。
Example 例证
Calculate an estimated accumulated total for when you retire. We will factor that we are going to start saving a few years after we graduate university and get a job. Lets predict we start our savings at age 25, and we want to retire at age 65. The Initial Principle invested will be ¥20,000. Each month you will contribute an additional ¥5,000 to your savings plan. Remember there are 12 months in a year and our formula factors in yearly contributions. The interest rate we will use is 3%.
估算一下当你退休后需要的存款。假如我们从大学毕业和找到工作之后开始存款，比如25岁，然后想在65岁时退休。存入的本金是￥20,000，然后每个月你打算存入￥5,000。记住一年有12个月，而我们的公式是按年存款来计算的。我们使用的利率是3%。
First we will need to convert all the information into the same format as our formula.
首先我们需要把所有的信息转变成如公式所示的形式。
n = “Retirement Age” – “Age Investment Starts”
n = “退休年龄” – “开始存款年龄”
n = 65 – 25
n = 40
c = “Monthly Contributions” X “Number of Months”
c = “每月存款” X “月份”
c = ¥5,000 X 12
c = ¥60,000
Now we will need to enter in all the information into our formula to calculate our Accumulated total for our Savings Plan. In the example we will only keep 2 decimal places. What is being calculated at each step in the example will be highlighted.
现在我们要把所有的信息输入公式里来我们的总金额了。如例所示，我们只保留2位小数，而且要标注出来。
A = P(1 + r)n + c [ {(1 + r)n – 1} / r ]
A = ¥20,000(1+0.03)40 + ¥60,000[ { (1+0.03)40 -1} / 0.03]
A = ¥20,000(1.03)40 + ¥60,000[ { (1.03)40 -1} / 0.03]
A = ¥20,000(1.03)40 + ¥60,000[ { (1.03)40 -1} / 0.03]
A = ¥20,000(3.26) + ¥60,000[ { (3.26) -1} / 0.03]
A = ¥65,200 + ¥60,000[ { (3.26) -1} / 0.03]
A = ¥65,200 + ¥60,000[ { (3.26) -1} / 0.03]
A = ¥65,200 + ¥60,000[ 2.26) / 0.03 ]
A = ¥65,200 + ¥60,000[ 75.33 ]
A = ¥65,200 + ¥4,516,800
A = ¥4,585,000
Therefore the proposed savings plan will result in ¥4,585,000 being saved for retirement. Now you will create your own Savings Plan.
最后我们得到结果：在我们退休时的总金额是 ¥4,585,000。现在你要创建你自己的储蓄计划了。
This formula only calculate cash assets being saved for retirement. What other types of assets might you have acquired by the time you are ready to retire?
该公式只能用来计算现金存款，那么当你退休时还有没有其他形式的资产？
Instructions 说明
Row 1: Leave blank
第1行：空白
Row 2: Merge Cells B-E and type the Main-Title
第2行：合并B-E单元格并输入主标题
Row 3: Leave blank
第3行：空白
Row 4: Merge Cells B-E and type the Sub-Title
第4行：合并B-E单元格并输入副标题
Row 5-7: Column B and C, type the English and Chinese descriptions
第5-7行：在B栏和C栏输入英文和中文的术语
Row 8: Leave blank
第8行：空白
Row 9: Merge Cells B-E and type the Sub-Title
第4行：合并B-E单元格并输入副标题
Row 10-14: Column B, C, and D, Type the English Chinese, and Formula descriptions
第10-14行：在B、C、和D栏输入中英文术语及公式首字母
Row 1-15 Column A-F: Format like the Example
第1-15，A-F栏：照例设计
Row18-23 Column D-F: Create a “Table” that shows the final “Accumulated Total”
第18-23，D-F栏：创建一个显示最终“计算金额”的表格
Cell E14: Enter the formula =P(1 + r)^n + c [ {(1 + r)^n- 1} / r ]
单元格E14：输入公式 =P(1 + r)^n + c [ {(1 + r)^n- 1} / r ]
Column E: Enter information into your Savings Plan spreadsheet to calculate your estimated savings based on the information you entered.
E栏：向储蓄计划表输入信息来估算储蓄金额。
Compare the results of your Savings Target and your Savings Plan.
比较以下你的储蓄目标表和储蓄计划表。
- Which is higher your Savings Target or your Savings Plan?
哪一个表的金额更高？ - What other assets might you acquire that are not accounted for in this project?
除了本项目中包括的资产，你还能获得哪些其他形式的资产？ - Summarize what you have learnt while completing these projects.
在完成这些设计之后，总结以下你所学到的。