# How to Calculate Compound interest

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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:

Suppose 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:

Suppose 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.

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