The compound interest formula can be used to calculate the principal and interest of an investment or deposit over multiple periods.

The basic form is: FV=PV x(1+r)^n, where FV represents the final return, PV represents the initial investment amount, r represents the interest rate, and n represents the number of periods.

The derivation of the compound interest formula is derived from the basic interest calculation formula. In simple interest calculation, interest is calculated based on the initial principal and is added to the principal at the end of each period. In compound interest calculation, the interest for each period is calculated based on the total amount of the previous period. This allows the interest to begin to have an exponential growth effect on the investment or deposit after a number of cycles.

Generally speaking, the compound interest formula can be calculated manually or using tools such as spreadsheet software. However, in practical applications, more complex calculations are required because the interest rate and number of periods often vary. For example, if the interest rate is floating, the different interest rates for each period need to be taken into account in the calculation. In addition, if there are multiple investments or deposits, then each item needs to be calculated separately and their sum will be used as the final return.

In the field of investment, the compound interest formula is often used to calculate the return on long-term investments. For example, if a person plans to have a certain amount of savings when he retires, he can put the money into a high-interest account and use the compound interest formula to calculate how much he should invest during his working life. This can help him get the expected benefits when he retires.

In addition to the investment field, the compound interest formula can also be widely used in other fields. For example, in credit card interest calculations, interest is usually calculated on a daily basis, and each month's balance becomes the basis for the next month. So when consumers want to calculate the growth rate of their credit card balance over several months, they can use the compound interest formula.

It should be noted that when using the compound interest formula, all variables and factors should be taken into account to ensure the accuracy of the calculation. Especially when calculating returns on long-term investments, you need to take into account inflation, taxes and other factors that may affect returns. Only with a thorough understanding and arrangement of these variables can you take full advantage of the advantages offered by the compound interest formula.