How should one accurately compute the interest earned over a period?

To accurately compute the interest earned over a period, one must consider the difference between the final and initial values of the investment or loan. This method involves determining how much the investment has increased in value over the specified time, effectively capturing the total gain attributable to interest.

When calculating interest, especially in the case of compound interest, simply multiplying the principal by the interest rate does not provide the complete picture, as it neglects the effect of previous interest being added to the principal. Similarly, summing all interest rates applied over the period may not accurately reflect the compounding that occurs, as interest can be applied differently at different times. Lastly, estimating based on averages from previous years does not give an accurate measurement of the current period's interest because it does not account for specific conditions or changes in rates.

By focusing on the total change in value—from the initial principal to the final amount—this approach encapsulates the compounded growth of the investment or loan, making it the most accurate means of calculating the interest earned over that specific time frame.