Compound Interest Formula

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 is the type of interest calculated on the initial principal, including all of the interest accumulated in the prior periods of a loan or a deposit.

The formula for computing Compound Interests is:

Where,

• P = Initial Principal
• i = Interest Rate
• n = Number of compounding periods, 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.

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 the 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

Example #2

Vardhan is looking to buy a new brand car on loan. The model which he liked will cost him the on-road price of 25,37,950.00. He can make an initial down payment of 10,00,000 and the rest of the amount he wants to be in the form of a loan. Bajaj finance is ready to provide him with 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 payments 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.  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 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.

Example #3

Shankar is interested in a new investment product that Invest Corp has recently launched. 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 the total income earned in this product assuming Shankar decides to invest in the same, and at the end of 15 years, the bonus income is 10,783.90.

We are given all the variables here: 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 the 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 multiply the same by the principal amount, yielding the interest that would either be earned or paid depending upon whether an amount is invested or a loan amount is taken.

Relevance and Uses

• Compound interest is the interest calculated on the initial amount invested, which is called the principal, which shall include all of the interest accumulated in the prior periods of a loan or deposit.
• Compound interest, as mentioned earlier, can be calculated by multiplying the initial amount invested, 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 1.
• 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 stock markets to estimate growth rates.

Compound Interest Formula calculator

You can use the following Compound Interest Calculator.

Recommended Articles

This is a guide to Compound Interest Formula. Here we discussed how to Calculate Compound Interest along with practical examples. We also have provided Compound Interest Calculator with a downloadable excel template. You may also look at the following articles to learn more –

1. Guide to Daily Compound Interest Formula
2. Calculator For Nominal Interest Rate
3. Examples of Simple Interest Rate
4. How to Calculate Interest Coverage Ratio?