Compound Interest
2026-02-28 09:02 Diff
https://brightchamps.com/en-us/math/commercial-math/compound-interest

Compound interest grows faster than simple interest because the interest earned in each period itself earns more interest. When the compounding frequency is high, we get a greater yield. We can calculate compound interest in first finding the final amount and then subtracting the principal from it. The value we get after we subtract the principal amount from the final amount is the interest. Let us learn how to find compound interest for different time periods next.

Compound interest formula for different time periods.

The formula for compound interest varies with the number of compounding periods per year. The formulas for different periods are given as;

1. Annual compounding: Here, the number of compounding periods per year is one.

\(A = P\left(1 + \frac{R}{100}\right)^{T} \)

2. Semi-annual compounding: Here, we compound twice per year. Hence, the number of compounding periods per year is two.

\(A = P\left(1 + \frac{R}{200}\right)^{2T} \)

3. Quarterly compounding: Here, we compound four times per year. Hence, the number of compounding periods per year is four.

\(A = P\left(1 + \frac{R}{400}\right)^{4T} \)

4. Monthly compounding: Here, we compound twelve times per year. Hence, the number of compounding periods per year is twelve.

\(A = P\left(1 + \frac{R}{1200}\right)^{12T} \)

5. Weekly compounding: Here, we compound fifty-two times per year. Hence, the number of compounding periods per year is fifty-two.

\(A = P\left(1 + \frac{R}{5200}\right)^{52T} \)

6. Daily compounding: Here, we compound for all the days of the year. Hence, the number of compounding periods per year is 365.

\(A = P\left(1 + \frac{R}{36500}\right)^{365T} \)

7. Continuous compounding: We use continuous compounding when the interest is added every moment. The continuous compound interest formula is given as;

\(A = Pe^{\frac{RT}{100}} \)