Future Value, Multiple Flows
Read this section. You will learn how to calculate the future value of multiple annuities.
To find the of multiple cash flows, sum the of each cash flow.
LEARNING OBJECTIVE

Calculate the Future Value of Multiple Annuities
KEY TAKEAWAYS
Key Points
 The of multiple cash flows is the sum of the of each cash flow.
 To sum the of each cash flow, each must be calculated to the same point in the future.
 If the multiple cash flows are a fixed size, occur at regular intervals, and earn a constant interest rate, it is an annuity. There are formulas for calculating the of an annuity.
Key Terms
 cash flow: The sum of cash revenues and expenditures over a period of time.
 annuity: A specified income payable at stated intervals for a fixed or a contingent period, often for the recipient's life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.
 incremental cash flows: the additional money flowing in or out of a business due to a project
Future Value, Multiple Cash Flows
Finding the future value () of multiple cash flows means that there are more than one payment/investment, and a business wants to find the total at a certain point in time. These payments can have varying sizes, occur at varying times, and earn varying interest rates, but they all have a certain value at a specific time in the future.
The first step in finding the of multiple cash flows is to define when the future is. Once that is done, you can determine the of each cash flow using the formula in. Then, simply add all of the future values together.
FV of a single payment: The FV of multiple cash flows is the sum of the future values of each cash flow.
Manually calculating the of each cash flow and then summing them together can be a tedious process. If the cash flows are irregular, don't happen at regular intervals, or earn different interest rates, there isn't a special way to find the total .
However, if the cash flows do happen at regular intervals, are a fixed size, and earn a uniform interest rate, there is an easier way to find the total FV. Investments that have these three traits are called "annuities".
There are formulas to find the of an annuity depending on some characteristics, such as whether the payments occur at the beginning or end of each period. There is a module that goes through exactly how to calculate the of annuities.
If the multiple cash flows are a part of an annuity, you're in luck; there is a simple way to find the . If the cash flows aren't uniform, don't occur at fixed intervals, or earn different interest rates, the only way to find the is to find the of each cash flow and then add them together.
Source: Boundless
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