Discounting refers to calculating the present value of a future sum.
Discounting is the inverse operation to compounding.
For example, suppose we invest $1,000 into an account that earns 10% per year for five years. We can find the value of the investment at the end of year five by calculating the compounding factor and then multiplying the compounding factor by the initial investment. The compounding factor is the sum of one and the interest rate, raised to the number of compounding periods. For this example, the compounding factor is 1.6105 ((1 + .10) raised to the 5th power), and the future value of the investment is $1,610.5 ($1,000 x 1.6105).
In the above example, the unknown value is the future value of the investment. However, suppose that we want to know how much to invest today to have $1,610.5 in five years when the investment is earning 10% per year? In this case, we divide the future value by the compounding factor. Dividing $1,610.5 by 1.6105 gives us $1,000.
To find the present value of a single sum, we perform the following: (1) Add one and the periodic interest rate. The periodic interest rate is the annual interest rate divided by the number of compounding periods in the year. If there is only one compounding period per year, then the periodic interest rate is the annual interest rate. (2) Raise this sum to the total number of compounding periods over the life of the investment. The total number of compounding periods is found by multiplying the total number of years by the number of compounding periods each year. If there is only one compounding period per year, then the exponent is the number of years. And (3) divide the future value by the result of step 2.