# Future value

Future value measures what money is worth at a specified time in the future. This is used in time value of money calculations.

To determine future value (FV) without compounding:

[itex]FV = PV *\ (1+rt)[itex]

To determine future value when interest is compounded:

[itex]FV = PV *\ (1+r)^t[itex]

where PV is the present value, t is the number of time periods, and r stands for the discount rate per time period.

For example, What is the future value of 1 money unit in one year, given 10% interest? The number of time periods is 1, the discount rate is 0.10, the present value is 1 unit, and the answer is 1.10 units. Note that this does not mean that the holder of 1.00 unit will automatically have 1.10 units in one year, it means that having 1.00 unit now is the equivalent of having 1.10 units in one year.

These problems become more complex as you account for more variables. For example, when accounting for annuities (annual payments), there is no simple PV to plug into the equation. Either the PV must be calculated first, or a more complex annuity equation must be used. Another complication is when the interest rate is applied multiple times per period. For example, suppose the 10% interest rate in the earlier example is compounded twice a year (semi-annually). Compounding means that each successive application of the interest rate applies to all of the previously accumulated amount, so instead of getting 0.05 each 6 months, you have to figure out the true annual interest rate, which in this case would be 1.1025 (you divide the 10% by two to get 5%, then apply it twice: 1.052.) This 1.1025 represents the original amount 1.00 plus 0.05 in 6 months to make a total of 1.05, and get the same rate of interest on that 1.05 for the remaining 6 months of the year. The second six month period returns more than the first six months because the interest rate applies to the accumulated interest as well as the original amount.

This formula gives the Future Value of an annuity (assuming compound interest):

FVannuity = ((((1+r)n) -1) /r) * (payment amount)

where r = interest rate; n = number of periods.

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