Calculating future value involves financial formulas and several variables, such as interest rates, time periods, and the principal or present value of the asset in question. When calculating future value for an ordinary annuity, a fourth variable is required, which is the regular payment that is to be received annually. Another consideration is the form of interest paid as it can be either simple interest or compound interest. With the former, interest can be earned on the principal only, whereas with the latter, interest can be earned on both the accumulated interest and the principal.
To illustrate, suppose one puts a principal of $500 US Dollars (USD) in a time deposit account that pays 5% compounded annually for three years. After the first year, the interest earned on the principal will be $25 USD, thus leaving a balance of $525 USD. This sum earns $26.25 USD at the end of the second year, therefore leaving a balance of $551.25 USD. Finally, at the end of the third year the interest earned will be $27.56 USD, which leaves a total balance of $578.81 USD. Therefore, the total amount of interest earned in the three year period is $78.81 USD.
Continuing with the above example, the interest earned annually in the simple form will be the same for three years. That is, $25 USD will be earned every year from year one to year three. This is because interest is only earned on the principal of $500 USD, and no interest is earned in year two on the previous year's interest of $25 USD, which is also the same case for year three. With simple interest, a total amount of $75 USD is earned as opposed to $78.81 USD with compound interest.
The practice of calculating future value as shown above necessitates financial formulas. When compounding interest rates apply, the formula used is as follows: FV = PV x (1 + r)^n. Where FV is the future value, PV is the present value or principal, r is the interest rate, and n is the number of time periods. Note that r is expressed in decimals unless a financial calculator is used. For example, 5% would be expressed as 0.05.
Understandably, the formula used with the simple interest rate method is different from when the interest is compounded.It follows as such FV = [(PV) x (r) x (n)] + PV, where the letters denote the same variables as above. For the example above, this formula would be used as follows: FV = [(500) x (0.05) x (3)] + 500, which gives $575 USD.
Furthermore, in calculating future value for a series of fixed payments per year, also called an ordinary annuity, another variable is needed, which is the amount received or paid annually. An example is a hypothetical annuity paying $200 USD annually for three years with a 5% interest rate. Its future value would be calculated using the following formula: FV = PMT [(1 + r)^n – 1] / r, where PMT is the annuity paid per year. Therefore, FV = 200 x [(1+0.05)^3 – 1] / 0.05, which gives 200 x [(0.1576) / 0.05] then 200 x 3.1525, finally arriving at $630.50 USD.
Moreover, when calculating future value where the interest is compounded more than once a year, a slightly different formula needs to be used. This is expressed as follows: FV = PV x [1 + (r / m)]^nm, where the letters represent the same variables as above with the addition of m, which denotes the times interest is compounded per year. To illustrate this, the first compounding example as above shall be used. This time, however, the interest will be compounded monthly instead of annually, which gives 12 compounding periods per year for three years. Thus, FV = 500 x [1 + (0.05 / 12)]^36, which arrives at $580.73 USD.
