# Formula for Future Investments Value

by Dennis Hartman

Understanding what an investment will be worth in the future, or how much it's likely to be worth, is a key part of investing. An educated estimation of what something will be worth can help you decide what to invest in. In some cases, investors can calculate with a high degree of accuracy what an investment's future value will be. This relies on a basic formula and several pieces of data.

## Terminology

Future investment value calculations rely on a number of different variables, each of which uses a standardized notation. Future value is represented as F or FV. The present value of the same investment is noted as P, V or PV. An investment's interest rate is represented as r and the duration of the investment is n or t, for time. Time must be measured in the same terms as the interest rate. For example, a bond with a 5 percent annual interest rate must use t in years to calculate future value, while a savings account deposit that earns monthly interest uses t to represent the number of months that the investment lasts.

## Formula

The basic formula for a future investment value uses all of the variables that describe the interest rate and duration. The first step of the formula is adding 1 to the rate r and raising the sum to an exponent of n, or time. Future value equals present value times the result of the first part of the equation. So, FV = P (1+r)^n.

## Accounting for Interest

The basic formula for future investment value covers many of the simplest cases of investments that have set interest rates and fixed durations. However, those who use continuously compounded interest require a different formula. This is the case when an investment earns interest, which is added back into the principal of the investment to make more interest in the next period. In cases of continuously compounded interest, the formula for future value is, FV = Pe^(rt). The lower case e refers to Euler's number (approximately 2.718) while r and t refer to the interest rate and time, respectively.

## Results

Determining future investment value allows an investor to compare two investment opportunities to calculate which will be worth more on a given date in the future. It can also tell an investor whether a particular investment will earn enough for an intended purpose. For example, a parent investing in a college savings plan for a child can place \$10,000 in the account, which has an annual interest rate of 5 percent, when the child is eight years old. When the child is 18, without compounding interest, the account will be worth \$16,289. If the parent wants to have \$20,000 to give the child for college, this savings plan isn't an adequate investment and one with a higher rate, and possibly more risk, may be a better option.

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