## Future Value, Multiple Flows

Read this section. You will learn how to calculate the future value of multiple annuities.

To find the $FV$ of multiple cash flows, sum the $FV$ of each cash flow.

#### LEARNING OBJECTIVE

• Calculate the Future Value of Multiple Annuities

#### KEY TAKEAWAYS

##### Key Points
• The $FV$ of multiple cash flows is the sum of the $FV$ of each cash flow.
• To sum the $FV$ 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 $FV$ 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 ($FV$) of multiple cash flows means that there are more than one payment/investment, and a business wants to find the total $FV$ 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 $FV$ of multiple cash flows is to define when the future is. Once that is done, you can determine the $FV$ of each cash flow using the formula in. Then, simply add all of the future values together.

$F V=P V(1+i)^{n}$

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 $FV$ 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 $FV$.

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 $FV$ 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 $FV$ 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 $FV$. If the cash flows aren't uniform, don't occur at fixed intervals, or earn different interest rates, the only way to find the $FV$ is to find the $FV$ of each cash flow and then add them together.

Source: Boundless