Future Value

Future value (FV) is the value to which a current asset will grow by a future date based on compounding interest. Put simply, FV is the future value of an asset adjusted for interest over time. It’s a useful tool for investors and financial planners to estimate how much an investment made today will be worth in the future, and this allows investors to make sound decisions.

Like many financial tools, future value is based on the time value of money concept, which states that a dollar today is worth more than a dollar at some time in the future.

So let’s say you invested $1,000 at a fixed interest rate of 6% for 10 years. At the end of those ten years, the $1,000 would be worth $1,790.85. Future value is a way to calculate how much that investment is worth today. It’s worth noting that the future value doesn’t account for high inflation or interest rate changes, which can impact an investment by reducing its value.

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

This is the most commonly used FV formula, which accounts for compounding interest on the new balance for each period. An initial investment of $1,000 at 10% annual interest would become a balance of $1,100 in year two, which would then also earn 10% interest. By the end of the third year, you would have a balance of $1,464.10 instead of a balance of $1,300 with simple annual interest which only calculates interest on the initial cash flow.

The formula for future value using simple annual interest is:

$$FV = C_{0} \times (1 + (r \times n))$$

Future Value Example

Kevin earns an interest rate of 2.2% on a $9,000 savings account. Let’s calculate the future value of this amount if Kevin keeps it for 11 years:

$$FV = \$9{,}000 \times (1 + 2.2\%)^{11} = \$11{,}434.11$$

Kevin also has account which he invested $20,000 into on January 1, 2017. The account has an annual rate of 11% and is compounded annually.

Since January 1, 2018, the terms of the account have changed and the compounded interest is not calculated twice per month. How does Kevin calculate the future value of the account on December 31, 2018?

First, we calculate the balance of the account as of January 1, 2018, before the new terms started.

• C₀ = $20,000
• Number of periods (n) = 4
• Annual interest rate = 11%
• Quarterly interest rate (r) = 11/4 = 2.75%

$$FV = \$20{,}000 \times (1 + 2.75\%)^{4} =\$22{,}292.43 $$

We now have the C₀ figure ($22,292.43) for the new twice-monthly compounding for 2018 and can calculate the future value.

• C₀ = $22,292.43
• Number of period (n) = 2 * 12 = 24 (twice a month)
• Annual interest rate = 11%
• Monthly interest rate = 11/12 = 0.0092
• Twice-monthly interest rate (r) = 0.0092/2 = 0.0046%

$$FV = \$22{,}292.43 \times (1 + 0.0046\%)^{24} = \$22{,}317.05$$

Future Value Calculator

You can use the future value calculator below to work out the FV of your own investments.