General Compound Interest Formula
To derive the general compound interest formula, let’s consider compounding interest n times per year.
If P is compounded n times per year at an annual interest rate r, the interest r is divided by n and applied n times per year. So, after t years, the formula becomes:
Where,
- represents the interest rate per compounding period.
- nt is the total number of compounding periods over t years.
This formula illustrates how the initial principal amount grows over time when interest is compounded at regular intervals. As n approaches infinity (i.e., continuous compounding), the formula converges toward the continuous compounding formula .
In summary, the compound interest formula is a result of the continuous compounding formula adapted for discrete compounding periods per year. It allows for the calculation of the future value of an investment or loan, factoring in compounded interest at regular intervals.
Compound Interest Formula
Compound Interest is the interest that is calculated against a loan or deposit amount in which interest is calculated for the principal as well as the previous interest earned.
The common difference between compound and simple interest is that in compound interest, interest is calculated for the principal amount as well as for the previously earned interest whereas simple interest depends only on the principal invested.
Table of Content
- What is Compound Interest?
- Compound Interest Formula
- How to Calculate Compound Interest?
- Compound Interest Formula – Derivation
- Half-yearly Compound Interest Formula
- Quarterly Compound Interest formula
- Monthly Compound Interest Formula
- Daily Compound Interest Formula
- Periodic Compounding Rate Formula
- Rule of 72
- Compound Interest of Consecutive Years
- Continuous Compounding Interest Formula
- Some Other Applications of Compound Interest
- Difference between Compound Interest and Simple Interest
- Compound Interest Examples
- Compound Interest – Practice Questions
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