# Future Value Interest Factor

## Did you know?

Future value interest factor (FVIF), also known as a future value factor, is a component that helps to calculate the future value of a cash flow that will be paid at a certain point in the future. The future cash flow could be a single cash flow or a series of cash flows (such as in the case of an annuity). Put simply, this factor helps us to determine the effect of compounding of a single cash flow or multiple cash flows (that occur at regular time intervals) in the future, per dollar of its present value and is based on the time value of money concept.

FVIF takes into account the compounding effect of money which states that as long as interest rates remain above zero, the value of money always appreciates over time. Therefore, FVIF is always more than one.

The future value factor is often available in the form of a table for ease of reference. This table usually provides future value factors for various time periods and discount rate combinations. So all you have to do would be to find out the factor listed at the intersection of interest rate and the time period and multiply this with the cash flow to find out the future value of this amount.

As was the case with the present value interest factor tables, the accuracy level of the future value factors listed in the future value tables is lower because of rounding. This means that the most optimal way to calculate the future value factor also would be to use the actual formula.

## Future Value Interest Factor Formula

$FVIF = (1 + r)^{n}$
• r = interest rate per period
• n = number of time periods

The two factors needed to calculate the future value factor are the time period and the interest rate.

The time period is essentially the time duration after which the money is to be received.

If the compounding period is one, use the given time period as n. If the compounding period is more than one, multiply the given time period by the compounding period to arrive at n.

The interest rate refers to the interest rate or the rate of return that an investment can earn in a particular time period.

Typically, the interest rate is provided in an annualized percentage rate (APR) basis. This means that to work out the rate needed for the calculation, you divide the given APR with the number of compounding periods per year to get the interest rate (r) for calculation of the future value factor.

To illustrate, if the APR is 8% with four compounding periods (m) per year for 2 years, then to calculate the FVIF:

• r will be equal to (APR/m)  = 2% (8%/4)
• n will be equal to n*m = 8 (2*4)

The formula for FVIF is derived from the future value formula:

$FV = C_{0} \times (1 + r)^{n}$
• C0 = Cash flow at the initial point (present value)
• r = rate of return
• n = number of periods

## Future Value Interest Factor Example

Situation 1: Paul deposits $1,000 in a bank for 2 years at 6% per year compounded annually. What will be the value of the money at the end of 2 years? Since the compounding factor is one, we only have 2 compounding periods, and the APR doesn’t need to be divided by the compounded periods, so it’s a simple FVIF calculation: $FVIF = (1 + 0.06)^{2} = 1.1236$ We can check this calculated FVIF of 1.1236 with the future value tables available for download. If we look up 6% and 2 years we see that the FVIF is 1.1236 which matches our calculation. Let’s now calculate the future value for the amount invested ($1000) using the future value formula:

$FV = 1000 * 1.1236 = \1{,}123.60$

Using the FVIF and the future value formula, we can calculate that the future value of Paul’s deposit at the end of 2 years would be $1,123.60. Situation 2: Let’s suppose that Paul deposits$1,000 in a bank for 2 years at 6% per year, but this time it is compounded semi-annually. What will be the value of the money at the end of 2 years?

In this example, it’s a little more complicated because the compounding factor is two periods per year. The number of periods, in this case, would be 4 (2 years * 2 periods per year) and the rate will be 3% (6% divided by 2 periods).

$FVIF = (1 + 0.03)^{4} = 1.1255$

Again, we can check this calculated FVIF of 1.1255 with the future value tables. We can also use the future value formula with the FVIF to calculate the future value:

$FV = 1000 * 1.1255 = \1{,}125.50$

The future value of Paul’s deposit at the end of 2 years would be $1,125.50 when the compounding happens semi-annually. ## Future Value Interest Factor Analysis Similar to the present value factor, the future value factor is also based on the concept of the time value of money and is used to estimate the value of an investment at a future point in time. Continuing with our above example, if Paul had to choose between the two options (annual compounding or semi-annual compounding) for investing his$1,000, all things beings equal, he will more likely choose option 2 (semi-annual compounding) since the future value of option 2 is slightly higher than that of option 1.

One major limitation with the future value concept is that it assumes a stable growth rate. But, the growth rate might vary depending upon the type of asset class. For instance, a bank deposit might provide a constant growth rate whereas an investment in a volatile asset class, such as the stock market, might yield varying rates of return, due to the inherent liquidity risk, inflation risk, and other political and economic risks.

Generally speaking, future value factor plays an important role in investment valuation and capital budgeting in real-life situations, since it allows an investor to determine the revenue generation potential of different investments. This will help him to make better investment decisions.

## Future Value Interest Factor Conclusion

To summarize, the following are some of the facts to bear in mind while using the future value factor:

• Future value factor is an integral component in the calculation of the future value of cash flows under the discounted cash flow model of investment valuation.
• It is based on the concept of the time value of money which stipulates that as long as interest rates remain above zero, the value of money always appreciates over time
• The three critical determinants needed for calculation of future value factor are time period, interest rate, and the compounding period
• Future value tables provide future value factors for different time periods and interest rate combinations for easy reference.
• Future value factor plays an important role in investment valuation and capital budgeting process.

## Future Value Interest Factor Calculator

You can use the future value interest factor (FVIF) calculator below to work out your own FV factor using the number of periods and the rate per period.