**Compound Interest Formula (Table of Contents)**

- Compound Interest Formula
- Examples of Compound Interest Formula (With Excel Template)
- Compound Interest Formula Calculator

## Compound Interest Formula

There are two types of interest one is simple interest and another one is compound interest. Compound interest can be defined as the type of interest which is calculated on the initial principal, that would include all of the interest which has been accumulated of the prior periods of a loan or a deposit.

The formula for computing Compound Interests is:

**Compound Interest = P * [(1 + i)**

^{n }– 1]Where,

**P**= Initial Principal**i**= Interest Rate**n**= Number of compounding period which could be daily, annually, semi-annually, monthly or quarterly.

**Examples of Compound Interest Formula (With Excel Template)**

Let’s take an example to understand the calculation of Compound Interest in a better manner.

#### Compound Interest Formula – Example #1

**Mr. A has deposited 100,000 in the FD where the bank pays 7% which is compounded annually. Mr. A wants to calculate compound interest that he would receive if he stays invested for 10 years.**

**Solution:**

Compound Interest is calculated using the formula given below

**Compound Interest = P * [(1 + i) ^{n }– 1]**

- Compound Interest = 100,000 * ((1 + 7%)
^{10}– 1) - Compound Interest =
**96,715.14**

#### Compound Interest Formula – Example #2

Vardhan is looking to buy a new brand car on loan. The model which he has liked will cost him on road price of 25,37,950.00. He can make an initial down payment of 10,00,000 and rest of the amount he wants to be in the form of a loan. Bajaj finance is ready to provide him a loan at a rate of interest of 11.88% which shall be compounded monthly. Vardhan wants the loan period to be of 5 years as he would be receiving equivalent payment in the future. So, he asks the banker to keep OD (overdraft) only for 5 years. Vardhan has asked the banker to compute what excess amount he would be paying for the loan. You are required to calculate compound interest for 5 years.

**We are given all the variables here that is P is 15,37,950 (25,37,950 -10,00,000), Rate of interest is 11.88% divided by 12 which is 0.0099 i.e 0.99% , n is 5 and frequency is 12 as its paying annually.**

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**Solution:**

Compound Interest is calculated using the formula given below

**Compound Interest = P * [(1 + i) ^{n }– 1]**

- Compound Interest = 1,537,950 * ((1 + 0.99%)
^{60}– 1) - Compound Interest =
**1,239,489.12**

The excess amount would be interested and that would be around 12 lakhs as he is paying out a loan and principal payment only at the end of 5 years.

#### Compound Interest Formula – Example #3

Shankar is interested in new investment product which has been recently launched by Invest Corp. The scheme asks to invest initially 50,000 and that will be matured after 15 years and the guaranteed rate of interest will be 9.72% which is tax-free and also it provides a bonus at the end of 15 years. Assume quarterly interest compound frequency. You are required to compute total income earned in this product assuming Shankar decides to invest in same and at the end of 15 years the bonus income is 10,783.90.

**We are given all the variables here that are P is 50,000, Rate of interest is 9.72% divided by 4 which is 0.0243 i.e 2.43%, n is 15 and frequency is 4 as its paying quarterly.**

**Solution:**

Compound Interest is calculated using the formula given below

**Compound Interest = P * [(1 + i) ^{n }– 1]**

- Compound Interest = 50,000 * ((1 + 2.43%)
^{60}– 1) - Compound Interest =
**161,154.51**

The income earned on this product will be 161,154.51 + 10,783.90 which is equal to 171,938.41.

### Explanation

To compute compound interest, we need to follow below steps.

**Step 1:** Find out the initial principal amount that is required to be invested.

**Step 2:** Divide the Rate of interest by a number of compounding period if the product doesn’t pay interest annually. Compounding frequency could be 1 for annual, 2 for semi-annual, 4 for quarterly and 12 for monthly.

**Step 3:** Compound the interest for the number of years and as per the frequency of compounding.

**Step 4:** Now deduct 1 from step 3 and then finally multiply the same by the principal amount which shall yield the interest that would either be earned or paid depending upon whether an amount is invested, or loan amount is taken.

### Relevance and Uses of Compound Interest Formula

- Compound interest is the interest which is calculated on the initial amount invested which is called as the principal, that shall include all of the interest which has been accumulated in the prior periods of a loan or deposit.
- Compound interest as mentioned earlier can be calculated by multiplying the initial amount invested called as the principal amount by 1 plus the annual rate of interest raised to the number or the frequency of compounding periods and subtracting it by one.
- When calculating compound interest, the number or the frequency of compounding periods will make a big difference or one can say a significant difference.
- These are used especially in banks, capital markets and also in stock markets to estimate growth rates.

### Compound Interest Formula Calculator

You can use the following Compound Interest Calculator

P | |

i | |

n | |

Compound Interest Formula | |

Compound Interest Formula = | P x [(1 +i)^{n} -1] |

= | 0 x [(1 +0)^{0}- 1] =
0 |

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