The Concept of Compound Interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
The basic formula for compounding is:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- A is the total future value.
- P is the initial principal.
- r is the annual nominal interest rate.
- n is the compounding frequency per year.
- t is the total duration in years.
By compounding more frequently (e.g. monthly or daily instead of annually), your wealth accumulates slightly faster because interest is computed and added to your balance sooner.