Earnings that is seen as payment for an investment or a price to pay for borrowing a sum of money, in the case where the earnings are periodically added to the previous capital or balance.

- Compound interest is often expressed in the form of a percentage of the borrowed sum to which the previous interest have been added.
- La valeur
*V*after_{n}*n*periods of an amount*M*invested at an interest rate*t*per period (a period being a duration at the end of which the interest is reinvested) is given by this relationship: \(V_n=M(1+t)^n\).

### Educational Note

The sequence of values of an amount that is earning compound interest illustrates a geometric progression.

### Example

If a person invests $500 in a savings account with a guaranteed interest rate of 5% per year, with interest added each month, the value of this investment will create this sequence of results:

502.08; 504.18; 506.28; 508.39; 510.50; 512.63; 514.77; 516.91; 519.07; 521.23; …