Compound interest refers to the interest that is calculated on the initial principal amount as well as any interest accumulated to date. In other words, it is not only the principal amount that earns interest, but also the interest that has accrued in previous periods.

The compound interest formula is as follows: **$A=P(1(n/r) _{nt}$**

Definition:

- $A$ is the final amount, including principal and interest
- $P$ is the initial principal amount (initial capital)
- $r$ is the annual interest rate (as a decimal)
- $n$ the number of interest periods per year
- $t$ the number of years

## Example

Suppose you invest €1000 at an annual interest rate of 5% and the interest is calculated annually (i.e. $n=1$) over a period of 10 years ($t=10$).

Insert these values into the formula:

- A = 1.000(1 (0,05/1)¹⁰
- A = 1.000(1 0,05)¹⁰
- A = 1.000(1,05)¹⁰
**A = 1,628.89 euros**

After 10 years, you will have a total of €1628.89, with compound interest making a significant contribution.

### The influence of more frequent interest calculation

The frequency with which interest is calculated can have a significant impact on the final amount. For example, if interest is calculated semi-annually, quarterly or monthly, the capital will grow faster.

Take the same example as above, but have the interest calculated quarterly ($n=4$). The calculation shows that the final amount would be higher in this case.

## Conclusion

Compound interest has an exponential effect on investments and can have a significant impact over long periods of time. It is crucial to understand this effect when assessing the potential value of an investment or savings account over time