Compound Interest Formula, is a numerical method to calculate the interest paid or interest received against a certain amount of capital borrowed or deposit for a defined interval of time at a specific rate of interest.

The special thing about compound interest is that it is always applied on the recent amount accumulated as a result of interest applied to the amount in the previous year. In simple way, we can say that it is the method of applying interest to the amount obtained as a result of interest applied during previous term or it is interest on interest.

$$A = P(1 + \frac{r}{n})^ {nt}$$

Where A is the total amount received, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded annually and t is the time in years.

We are quite familiar with the term interest because of its extensive use in daily life while going through different sort of transactions that involve capital or assets. Whether, we are depositing some amount in our bank’s saving account for future planning or we are taking loans from a bank for business investments we do give ample amount of weight to the consideration of interest rate before making our final decision.

The very term interest plays essential role in determining the cost of borrowing or benefit of depositing money in a bank or in varied sort of financial transactions. There are different types of interest which find their use in our financial markets and as a result different formulas are used to calculate it. But, for today, we will focus on Compound Interest Formula.

The concept of interest finds its basis in the concept of Time Value of Money, which can be simple put forward as follows:

As the time passes, the inherent value of different financial assets or capital does not remain constant, rather this value decreases in most cases. The decrease in the value of assets is dependent on varied factors in financial markets which play a vital role in determining the future value of an asset. As a result of this decrease in the value of assets or capital the concept of interest is incorporated in financial transaction in order to cater the depreciation or devaluation of capital or assets.

Note:  It must not arise any confusion that Compound Interest Formula essentially provides compensation against the overall decrease in the value of an asset.

### Uses of Compound Interest in Real Life

The concept of compound interest has rigorous use in business, banks and other areas of finance. Some of its very common usages are listed below:

• Most companies pay pension to their employees at the end of their careers. What actually happens is that companies open an account of employee and a certain chunk of the salary of employees is deducted and deposited to that account each month. That amount is invested in different sectors where a good return is guaranteed. So, at the time of retirement the employee is paid the total sum along with compounded interest.
• Insurance companies also use this formula to pay insurance amount to their subscribers.

#### Examples

Adam deposited $3,000 in a bank 3 years ago on interest rate of 7% which is compounded semi-annually. Now, he wants to withdraw the amount in order to pay fee of his graduate school. Calculate the total amount that is received by him from bank. • Principal Amount = P =$ 3,000
• Rate of interest = r = 7 % = 0.07
• Number of years = t = 3
• Number of times Interest is compounded annually = n = 2
$$A = P(1 + \frac{r}{n})^ {nt}$$ $$A = 3,000(1 + \frac{0.07}{2})^{2 \times 2}$$ $$A = 3,000(1 + 0.035)^4$$ $$A = 3,000(1.035)^4$$ $$A = \ 3442.6$$

So, Adam will receive \$3442.6 after three years.

### Alternative Formulas

The compound interest described above is commonly used to calculate the total amount returned after a specified time period against an initial investment which is compound at a fix rate. However, another formula is used to calculate the compound interest separately which is then added to the initial amount to calculate the total amount returned. The formula is represented as:

$$C = P[(1 + \frac{r}{n})^ {nt} - P]$$

Where C is the compound interest.

So, to conclude one can always use the formula given in the start to calculate the total amount returned after compound interest or one can calculated the compound interest separately and add the initial amount to it in order to find the total amount returned.