The term you're looking for is Compound Interest.
Here's a detailed explanation:
1. Understanding Interest: Interest is the cost of borrowing money, usually a percentage of the amount borrowed or invested.
2. Simple Interest vs. Compound Interest:
- Simple Interest is calculated on the principal amount of a loan or deposit. It doesn't change and is not reinvested.
- Compound Interest, on the other hand, is calculated on the initial principal, which also includes all the accumulated interest from previous periods.
3. How Compound Interest Works:
- When you invest or save money, you earn interest on the initial principal (the original amount of money).
- In the next compounding period, the interest is added to the principal. Now, the new principal is the original amount plus the interest earned from the previous period.
- This process repeats, and thus, each period, you earn interest on a larger and larger principal amount because it includes all the previously earned interest.
4. Example:
Let's say you invest [tex]$1000 at an interest rate of 5% per year, compounded annually.
- After the first year, you earn $[/tex]50 in interest, so you now have [tex]$1050.
- The next year, you earn interest on $[/tex]1050, which gives you an additional [tex]$52.50. So, at the end of the second year, you'd have $[/tex]1102.50.
- This process continues, and the amount grows because you are earning interest on the principal and the accumulated interest.
Therefore, the correct term for when interest is added to the principal, so that the interest that has been added also earns interest, is Compound Interest.
