# Future Value

## Definition

The term future value is used to describe the worth of an asset at a later time.  Future value is a nominal sum of money received in the future, assuming a given rate of interest earned.

### Calculation

Future Value (Simple Interest Formula) = PV x (1 + (R x T))

Where:

• PV = the present value of the asset
• R = the rate of interest earned in each period
• T = the fraction, or number of periods, the interest is earned

Future Value (Compounding Formula) = PV x (1 + R)T

Where:

• PV = the present value of the asset
• R = the rate of interest earned in each period
• T = the number of periods over which the interest is earned

### Explanation

As the name implies, future value provides the analyst with insights into the worth of an asset at a future point in time.  Unlike present value calculations, future value is not corrected for inflation and is stated in nominal dollars.

A future value calculation is frequently performed when investors want to understand the value of their money at a later date.  This calculation can be performed using a simple interest or compounding formula:

• Simple Interest:  involves applying the rate to principal only
• Compounding Interest:  involves applying the rate to both principal and interest that has been earned but not yet paid or withdrawn

### Example

Lindsey has the choice between two investments.  She can place \$10,000 in Fund A for five years, promising simple interest of 10% per year.  Alternatively, Fund B promises to provide a return of 9.50% compounded monthly for five years.  Lindsey would like to determine the future value of each investment:

Fund A (Simple Interest)

= \$10,000 x (1 + ( 0.10 x 5))
= \$10,000 x (1 + 0.5)
= \$10,000 x 1.500, or \$15,000

Fund B (Monthly Compounding)

= \$10,000 x (1 + 0.095/12)5 x12
= \$10,000 x (1 + 0.007919)60
= \$10,000 x 1.605, or \$16,500

Note:  In this example, monthly compounding requires the interest rate to be stated in months (9.5% / 12, or 0.007919) as well as the number of periods (12 months x 5 years, or 60 months)