Future Value is largely the same as present value but in reverse. The basic idea is the same except here instead of determining what something is worth today, we want to find out how much something is worth in the future. For example how much will I have if I invest today. 

The basic formula is 

(8) FV = 

Example: you invest $1000 today at 10% in one year you will have 1000*(1.1)¹=$1,100

In two years you will have 1,000*(1.1)²= 1,210. In three years you will have $1,331, This is based on the implicit assumption of compound interest. Which means you earn interest on your interest. This is a powerful concept and can lead to very large amounts when you have enough time periods over which to accumulate more interest.

Like in the present value discussion we also can use tables to determine a future value factor. Table A3 gives us future value factors. These are abbreviated as FVIF(r,n). Thus 

FV  = PV * (FVIF(r,n)) If r=10%, n=3

        = $1,000 * 1.331 = $1,331 which is the same we calculated above.

We also have annuities when calculating future values. These are often used in retirement planning. For example if you invest $1000 a year for three years how much will you have at the end of three years? Use table A4. If r=10%, n=3 (as before)

FV   = CF * (FVAF(r,n)) 

        = $1000 * 3.3100

        = $3,310.00 

How is the future value of an annuity calculated? (that is where are the numbers coming from?) Remember the future values for single payments at 10% for 1 and 2 years these plus the last payment of $1000 sum to $3310. Still uncertain as to the logic? Draw a timeline. Your first payment occurs at the end of year one and earns interest for two years ($1210), the second cash flow occurs at the end of the second year and earns interest for 1 year ($1100), while the third cash flow occurs at the end of the third year and therefore earns no interest ($1000).

When planning your retirement you must account for inflation. We generally use the nominal rate of interest. Thus although you may have a million dollars in the future, that money will be worth less than a million dollars today. For evidence of the effects of inflation consider that a $1 in 1940 is now worth only 8.5 cents (if we believe the CPI numbers-but that is another story). For more information on this, you might want to check http//ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

Retirement planning is one of the most common ways that future value is used.  For notes on this and to see how Ben Franklin  used compounding see FinanceProfessor's Retirement planning page.