# How to Calculate Discrete Returns

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Discrete numbers and investments have a distinct set of possible values rather than a continuous set. In other words, the number can only be an integer or some predefined value. The normal number line of investment returns is continuous with infinite number of values (1, 1.1, 1.01 etc.). Calculating a discrete return makes the number much more concrete. A common discrete return is a compound interest rate.

Find the amount of principal that you will form as the base point for your investment returns. If it is a loan, the principal is the total loan amount minus any down payment. For example, a $60,000 loan that was initially paid down with$10,000 will yield a $50,000 principal. Use the rate of interest to help calculate discrete returns. Based on the level of risk of the borrow and the type of loan, the interest rate will vary substantially. Assume a 12 percent risk for this example. Use the formula for discrete returns to find the annual rate of compounding. The formula is 1 plus the interest rate divided by the number of times compounded annually raised to the power of the number of annual compounds. If the loan is compounded twice per year the equation would be: Discrete return = (1+.12/2)^2 = (1+.06)^2 = 1.1236 Determine the total discrete return by multiplying the principal by the result from Step 3. So,$50,000 X 1.1236 = \$56,180.