What is Continuous Compounding?
Continuous compound interest refers to the interest rate obtained under the limit of the number of periods approaching infinite. At this time, the interval between different periods is very short and can be regarded as an infinitesimal quantity. Compound interest is compound interest, which means that the annual income can also generate income. Specifically, the entire borrowing period is divided into several sections. The interest calculated based on the principal in the previous section is added to the principal to form an increased principal. As the principal base for calculating interest in the next paragraph, until the interest in each paragraph is calculated, after adding up, the interest over the entire borrowing period is obtained, which is simply known as profit rolling.
Continuous compounding
discuss
- Chinese name
- Continuous compounding
- Foreign name
- continuously compounding interest
- Definition
- Get the interest rate when the number of periods approaches the infinite limit
- Subject
- economics
- Continuous compound interest refers to the interest rate obtained under the limit of the number of periods approaching infinite. At this time, the interval between different periods is very short and can be regarded as an infinitesimal quantity. Compound interest is compound interest, which means that the annual income can also generate income. Specifically, the entire borrowing period is divided into several sections. The interest calculated based on the principal in the previous section is added to the principal to form an increased principal. As the principal base for calculating interest in the next paragraph, until the interest in each paragraph is calculated, after adding up, the interest over the entire borrowing period is obtained, which is simply known as profit rolling.
- definition
- Continuous compounding
- In extreme cases, the principal C0 calculates interest at compound interest for an infinitely short period of time.
- Assuming the current interest rate is and e is a natural constant, the final value of the investment FV = C0 × e ^ (t) after T years of investment.
- Continuous compounding
- Relationship between annualized percentage return and effective annual interest rate:
- EAR effective annual interest rate,
- r Annualized percentage interest rate.
- Relationship between real interest rate, nominal interest rate and inflation rate:
- Real interest rate R
- Nominal interest rate r
- Inflation rate i
- In other cases
- But it is the identity under continuous compound interest: