Calculating the annual equivalent of a daily charge or per diem interest, or compounding annual growth based on daily interest, can help you estimate your company's earnings, find the value of its investments or see how much penalty interest you may earn on a client's unpaid invoice. Not all of these calculations produce results that scale accurately to predict actual earnings, but they can offer useful insight into potential outcomes.
Calculating Earnings
To translate a daily wage or service rate into an annual income, multiply your earnings figure by the number of working days in a year. To calculate the workday total, multiply the 52 weeks in a year by the five working days in a regular work week, deriving 260 days as a raw result. Subtract the number of holidays you observe to calculate the net number of working days. Once you know the number of days on which you can bill your daily rate in a year, you can multiply your daily rate by that total.
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Annualizing Growth
If you earn a specific amount of gain on an investment in a certain number of days, you can extrapolate how much you'd earn if that rate applied for an entire year. Divide the amount you earned by the amount you invested to derive the decimal rate of return and add one to that value. Divide 365 by the elapsed number of days and apply the output of this second calculation as an exponent to the output of the first calculation. Subtract one from the result to derive your annualized return. Expressed mathematically, this calculation takes the following form: ((1 + decimal rate of return) ^ (365 / elapsed days)) - 1
Compound Annual Growth
Simple interest calculations fail to take into account the fact that the amount to which earnings apply increases with each incremental application of the interest rate. Compound calculations factor in these earnings to reflect annualized earnings more accurately. Divide your daily interest rate by 100 to make it a decimal value. Next, add one and raise the result to the 365th power. Subtract one and multiply by 100 to turn your calculation back into a percentage. The result equals an annualized compound interest rate, based on a constant daily earnings rate. In mathematical symbols, that calculation looks like this: ((((daily interest rate / 100) + 1) ^ 365) - 1)
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Other Considerations
Extrapolating annualized gains from short-term daily performance makes some assumptions that may prove unrealistic over the course of an actual year of financial results. Assuming that you can bill out your daily rate on every potentially billable day might not match your actual results unless you hold a contract that guarantees your company a steady flow of work. Assuming that a daily interest rate doesn't change over the course of a year also may create overly optimistic results, unless the rate stems from a binding agreement.
References
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