# What is a Future Value?

The future value is how much a certain amount of money today will be worth in the future if invested at a known interest rate. It is calculated using the time value of money equation based on interest rates and present values. Common variations are the future value of an investment earning simple interest, an investment earning compound interest and of an annuity.

The idea behind the future value of money is that $1,000 US Dollars (USD) today is worth more than $1,000 USD a year from now. This is because the money can be placed in a savings account or some other investment and will gain interest during the year. This is called the time value of money and is used in many investment schemes from savings accounts and pension plans, to lottery jackpots that give annual payouts.

The simplest formula of a future value (FV) is an investment that earns simple interest. The present value (PV) is the amount that is to be invested today. The interest rate (i) is the annual interest rate. Time (t) is the length of time in the future that is to be calculated. The formula is: FV = PV*(1 + i*t).

Simple interest is rarely used in real life applications where compound interest is much more common. The formula for the future value of an investment with compound interest is: FV = PV*(1+i)^{t}. For example, if the original investment amount is $2,000 USD, the investment rate is 4%, and the investment is for ten years, then the future value FV = 2000*(1+.04)^{10} = $2,960.49 USD. This means that the $2,000 USD today is worth $2,960.49 USD in ten years, given a 4% interest rate.

Interest rates will fluctuate over a ten year period. If the interest rates rise to 8%, then a new investor could buy a similar product as the above example and the future value of the new investment product would be $4,317.85 USD. The first investment, whose interest rate is locked in at 4% for ten years, is less attractive, and would be sold at a discounted rate. If the interest rates fall below 4%, the initial investment is considered above par and will trade for a higher value.

Annuities are financial products that provide regular payouts at a fixed interest rate. The simplest forms of annuities are regular deposits to savings account paying monthly interest and mortgages with monthly payments on the principle and interest. To calculate the future value of an annuity (FV) with payout (A), interest rate (i), and time period (n), the following formula is used: FV = (A * ( 1+i)^{n}-1)/i.

Life annuities are funds that are fed and grow over a certain amount of time when they start paying out a steady stream of income, usually for retirement. Future values are carefully studied when pricing life annuities and many assumptions are required, such as retirement age and interest rates. The commuted value of a pension fund, a type of life annuity, is the amount of money necessary to fulfill a pension contract when payouts start and is based on the life annuity future values.

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