part 2 2-1 future value -single amount

2. future value-single amount(一次款项复利终值）

In determining the future value, we measure the value of an amount that is allowed to grow at a given interest rate over a period of time. Assume an investor has 1000 and wishes to know its worth after four years if it grows at 10 percent per year. At the end of the first year, the investor will have 1000*0.1+1000=1100. by the end of year two, the 1100 will have grown to 1100*1.1=1210. this process of earning more interest on a previous period’s interest is called compounding. The four year pattern is indicated here:

1st year  1000*1.1=1100

2nd year 1100*1.1=1210

3rd year 1210*1.1=1331

4th year 1331*1.1=1464.1

After the fourth year, the investor has accumulated 1464. because compounding scenarios (设想、可能发生的）often cover a long period, a more generalized formula is necessary to describe the compounding procedure, we shall let FV=FUTURE VALUE, PV=PRESENT VALUE, I=INTERST VALUE,N=NUMBER OF PERIOD 

The simple  formula is:

FV=PV(1+I)N

IN this case, PV=1000, I=10%,N=4, SO we have:

FV=1000(1.1)4,or 1000*1.4641=1464.1, and the 1.4641 we can obtain through table.

Because the future value equation is simple,you will probably find that calculating the future value of a single amount can be done easily using this equation. However, some students will prefer to use a spreadsheet to do these calculations. 

Although the future value of a single amount is straightforward, we will encounter cash flow patterns that are more complicated. To organize those cash flows and other information in a useful manner, you will need to use a timeline. Using timelines is an excellent habit to form. Many of the early examples shown will probably seem so simple that a timeline adds little to your organizational abilities. However, by forming this good habit early, you will be much more competent and confident when you begin to encounter more difficult concepts.

With this in mind, consider the following timeline:

The intervals between each of the periods represent the number of years. The number “2” labels the end of the send year, and the label ”4”: marks the end of the fourth year. Notice that the period markers are at the end of each year.

Cash flows are shown above the timeline. The present value of 1000 grows at 10% for years to the future value of 1464.1.

One concept that may be difficult to grasp is that a number marks the end of a period, but it also marks the beginning of another period. For example, the number “2” marks the end of the second year, but this is also the beginning of the third year. Likewise, the end of the third year will coincide with the beginning of the fourth year, therefore, the beginning of the fourth year is labeled”3” on the timeline. We will address a few details concerning how to use the financial calculator after we see an example. Let’s consider the future value problem we saw in this chapter. What is the future value of 1000 if it is invested at 10% and compounds for 4 years?