Future Value with Multiple Cash Flows

Suppose you deposit $100 today in an account paying 8 percent. In one year, you will deposit another $100. How much will you have in two years? This particular problem is relatively easy. At the end of the first year, you will have $108 plus the second $100 you deposit, for a total of $208. You leave this $208 on deposit at 8 percent for another year. At the end of this second year, it is worth:

Figure 6.1 is a time line that illustrates the process of calculating the future value of these two $100 deposits. Figures such as this one are very useful for solving complicated problems. Almost anytime you are having trouble with a present or future value problem, drawing a time line will help you to see what is happening.

In the first part of Figure 6.1, we show the cash flows on the time line. The most important thing is that we write them down where they actually occur. Here, the first cash flow occurs today, which we label as Time 0. We therefore put $100 at Time 0 on the time line. The second $100 cash flow occurs one year from today, so we write it down at the point labeled as Time 1. In the second part of Figure 6.1, we calculate the future values one period at a time to come up with the final $224.64.

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