**Compound interest is a type of interest that is calculated on both the principal amount and the accumulated interest of a loan or investment. The formula for calculating compound interest is:**

### Compound Interest = P (1 + (R / N))^(N x T) - P

**Where:**

P = principal amount (the amount of money borrowed or invested)

R = annual interest rate (expressed as a decimal)

N = number of times the interest is compounded per year

T = time period (in years)

Using this formula, you can calculate any of the following variables given the other three:

P = C / (1 + (R / N))^(N x T)

R = N[(C / P)^(1 / (N x T)) - 1]

N = log[(C / P) / (1 + R / N)] / (T x log(2))

Where C is the final amount including principal and interest, and log is the natural logarithm.

### Here are some examples of how to use the compound interest formula:

**Example 1:**

**Suppose you invest ₹5,000 at a compound interest rate of 6% per annum, compounded monthly, for 5 years. What will be the total amount you will receive at the end of the investment period?**

**Solution**

Compound Interest = P (1 + (R / N))^(N x T) - P

Compound Interest = 5,000 (1 + (0.06 / 12))^(12 x 5) - 5,000

Compound Interest = ₹6,771.32

Therefore, the total amount you will receive at the end of the investment period is ₹6,771.32.

**Example 2:**

S**uppose you borrow ****₹10,000 at a compound interest rate of 8% per annum, compounded quarterly, for 3 years. What will be the total amount you will have to repay at the end of the loan period?**

**Solution**

Compound Interest = P (1 + (R / N))^(N x T) - P

Compound Interest = 10,000 (1 + (0.08 / 4))^(4 x 3) - 10,000

Compound Interest = ₹12,597.73

Therefore, the total amount you will have to repay at the end of the loan period is ₹12,597.73.

**Example 3:**

S**uppose you want to invest ****₹3,000 at a compound interest rate of 5% per annum, compounded semi-annually, to reach a target amount of ₹5,000 in 4 years. What will be the interest rate you need to achieve your target?**

**Solution**

Compound Interest = P (1 + (R / N))^(N x T) - P

5,000 = 3,000 (1 + (R / 2))^(2 x 4) - 3,000

2.5 = (1 + (R / 2))^(8)

log(2.5) = 8 log(1 + (R / 2))

log(2.5) / 8 = log(1 + (R / 2))

1.05 = 1 + (R / 2)

R = 0.1 = 10%

Therefore, you need an interest rate of 10% per annum, compounded semi-annually, to reach your target of ₹5,000 in 4 years.