Compounding, future value

Compounding is the process of finding an unknown future value from a known present value. Using a time line, compounding is moving forward in time from the present to some point in the future. Given the time value of money (assuming that INTEREST RATES are always positive), future values are always larger than present values. For deposits and other INVESTMENTs where interest can, in turn, earn interest, compounding can be quite powerful, especially at higher rates of interest. Because INFLATION builds upon itself—that is, it compounds—uncontrolled inflation is quite damaging to the value of money and its PURCHASING power. For a lump sum, the future value of some present amount is determined by the compounding formula FVn = PV[1+ir]n, where FVn is the future value at some future point in time n, PV is the present value (the current amount of the lump sum), ir is the interest rate (expressed in decimal form) applicable to the situation in question, and the exponent n is the same future point in time for which the future value is to be determined. For instance, find the future value in three years of a current deposit of $100 at 10 percent compounded annually: FV3 = 100 [1.10]3. Simplifying the formula reduces this to FV3 = 100[1.331] = 133.10. Notice that 10 percent of $100 is $10, yet the future value adds more than $10 interest per year for three years to the lump sum. Compounding (interest earning interest) added $3.10 to this lump sum over three years. It is sometimes necessary to determine the future value of an ANNUITY. While there is a formula for this, it is much easier to use a commonly published table of interest factors. For compounding, there are tables of future-value interest factors for lump sums (FVIFs) and for annuities (FVIFAs). To find the future value of a lump sum: FVn = PV[FVIFi,n], where FVIF is the lump-sum future-value interest factor for some interest rate i and for some time period n. To find the future value of an annuity: FVAn = PMT[FVIFAi,n], where PMT is the regular annuity payment and FVIFA is the annuity future-value interest factor for some interest rate i and for some time period n. While using the published tables of future-value interest factors is easier than manually doing the numbercrunching, it is much more convenient to find future values for lump sums and annuities using a financial calculator. Remembering that the interest factor tables carry the interest factors to only four digits to the right of the decimal, the results obtained from the use of a financial calculator are more accurate than using the tables. The published interest factor tables list interest factors only for whole-number interest rates. A financial calculator can compound using any interest rate.
See also RULE OF 72.