The formula for the future value is based on a table that shows the growth of the investment on a period by period basis. Let "B" represent the initial balance for any given period.
periodic interest = Bi
final balance = B + Bi = B(1 + i)
For any given row in the table, the final balance is found by multiplying the initial balance by (1 + i). Applying this principle to the table leads to an obvious pattern.
The final balance in each row has a similar form with the exponent equal to the period number. The final balance in the last row is the future value of the investment.
Solving this formula for the present value yields:
The interest earned is simply the difference between the amount invested (present value) and the future value.
