### What is Future Value?

The value of an asset or investment at a specific time or date in future is called Future Value (FV). It is the amount to which an investment or a series of investments will grow by a specified date and time in future and will be received after T years or periods.

Future value is based on an assumed rate of interest, or more generally, a rate of return. If, based on a guaranteed or assumed rate of return or interest rate, a $1000 investment made today will be worth$10,000 in 20 years, then the Future Value of the $1000 investment is$10,000.

The Future Value equation assumes that there is a constant rate of growth. It also assumes that the single upfront payment is left untouched for the entire duration of the investment for which the value is calculated. It must also be kept in mind that the value does not include corrections for inflation or other factors that affect the true value of money in the future.

Keeping in view the concept of “Time Value of Money”, the Future Value (FV) is expected to be higher than the Present value (PV).

### The Future Value Formula

The formula for calculation of Future Value depends on the type of interest being earned: Simple Annual Interest or Annual Compound Interest.

#### Simple Annual Interest Future Value Formula

Simple annual interest is rarely used when calculating Future Value, because compounding is considered to be a more meaningful formula, but in case you need to calculate simple interest, the formula for calculation of FV will be as follows:

$$FV = PV \times (1 + rt)$$

Where:

FV = Future Value of Investment

PV = Present Value of Investment

r = Rate of Interest

t = Time in years/periods for which investment will be held

For instance, if $100 is invested for 5 years with a simple annual interest of 10%, the future value of this investment would be$150.

#### Compounding Annual Interest Future Value Formula

$$FV = PV \times (1 + i)^{t}$$

Where:

FV = Future Value of Investment

PV = Present Value of Investment

i = Rate of Interest

t = Time in years/periods for which investment will be held

For instance, if $100 is invested for 5 years with an interest rate of 10%, compounded annually, the future value of the investment would be$161.051.

### Uses of Future Value Formula in Finance

The Future value formula can be applied to various areas of Economics & Finance including corporate finance, financial economics, and investment finance, and has a wide range of uses.

The Future Value calculation allows researchers and investors to predict, with varying degrees of accuracy, the amount of profit that can be generated by different investments. The amount of growth generated by holding a given amount in cash will likely be different than if that same amount were invested in stocks, so the FV equation is used to comparatively analyze the multiples options available.

Depending on the type and nature of an investment, calculating the FV of an asset can become complicated. In addition, the calculation of FV is based on the assumption of a stable rate of return. If the interest rate is guaranteed on an investment, as in the case of a savings account, then it is relatively easy to calculate the Future Value accurately. However, in cases of investments where the rate of return is more volatile, as in the stock market or other securities, the calculation of Future Value can present greater difficulty and complexity.

Although calculating future value has its utility, it is important to remember that future value does not include fluctuating interest rates, adjustments for inflation, or fluctuating currency values that are likely to affect the true value of the investments in the future.

#### Example 1

A salaried individual would like to determine his ending balance after the end of five years on an account that earns 10% per year. $1000 is the original balance on the account. Solution: Present value (PV) =$1000

Rate of interest (R) = 0.10 (10%)

Time Periods (T) = 5 (years)

Putting this into the formula, we would have:

FV = PV * [1 + (R * T)]

= 1000 * [1 + (.10 * 5)]

After solving, the ending balance after 5 years would be $1500. #### Example 2 A salaried individual would like to determine his ending balance after the end of one year on an account that earns 0.5% per month and is compounded monthly.$1000 is the original balance on the account.

Solution:

Present value (PV) = $1000 Rate of interest (R) = 0.005 (0.5%) Time Periods (T) = 12 (months) Putting this into the formula, we would have: FV = PV * [(1 + R)T] = 1000 * [(1+.005)12] After solving, the ending balance after 12 months would be$1061.68.

It is interesting to note that 6% of $1000 is$60. The additional \$1.68 earned in this example is due to compounding.

### Alternate Future Value Formulas

$$FV = C_{O} \times (1 + r)^{n}$$

Where;

C0 = Cash flow at the beginning

r = rate of return

n = total number of periods