# What are Compound Interest with Explanation

## Compound Interest Definition

Compound Interest is an interest on a deposit, which based on both the principal amount and the accumulated interest from previous period. In easy words, It is the interest earned on interest.

## Detail Explanation of Compound Interest

As the compound interest name itself suggests that interest paid in case of loan, and earned in case an investment. That earned interest is sporadically added to the principal amount. Thus, interest is earned on interest as well as the initial principal. It is compounding of interest or compounding effect that accounts for the melodramatic alteration between simple and compound interest. You can compound interest on different frequency schedules such as daily, monthly or annually. The more the number of compounding periods, more will be the compounded interest.

Let us consider with an example, if you deposit an amount of money in saving account with a compound interests in any commercial banks in United States, the longer you keep money in that account, the faster will be the your saving grow, because you will earn returns on the money you invest, as well as on returns at the end of every compounding period, because, the more the number of compounding periods, more will be the compounded interests earned. Now it depends on Banks, that how much interest rate they set for, and how much years you keep your money in saving account, and how many compounding period will you set for.

Suppose you are depositing \$10,000 at Axos Bank High Yield Savings bank in San Diego, California, United States, at the compound iinterest rate of 10%, annually compounded, for 20 years.  Here, after 1st year on \$10,000 you will earn 10% compound interest of \$1000, means in your saving account it will be total \$11,000 now, (\$1000 + \$10,000). In 2nd year you will earn another 10% compound interest on \$11,000, means in your saving account it will be total \$12,100 (\$11,000 + 1100). Similarly, it will repeated and at the end of 3rd   year, you will have total of \$13,310 in your saving account of Axos Bank High Yield Savings bank. It’s also worth mentioning that there’s a very similar concept known as cumulative interest.  You will be understood more clear in the table below:

 Time Period Compound Interest @ 10% (Annually Compounded) Difference of Compounding Than Simple Interest Principal Amount \$10,000 1st Year \$11,000 (\$1000 earned) 2nd Year \$12,100 (\$1100 earned) \$100 3rd Year \$13,310 (\$1210 earned) \$110

Here,  you can see the difference each year interest earned is more than previous year in compound interest, while in simple it would have been the same as the previous year. That is why it is used extensively to earn profit by investors in banks.

Extensive variation of problems in finance can be resolve using this concept of compound interest.

### What is the Compound Interest Formula

CI = P (1 + r/n)^(nt)

Compound Interest Formula

Whereas,

CI = Compound Interest

P = Principle Amount

r = Interest Rate

n = Number of Times Interests Applied per Time Period

t = Number of Time Period

## Problem on Compounding Interest

If \$30,000 is invested in Axos Bank High Yield Savings bank at 10% p.a. for 5 years, what will be the Future value at the end of 5th year?

Solution:

Data

P = \$30,000

r = 10% = 10\100 = 0.1

t = 5 years

n = 1

CI = ?

According to Formula,

CI = P (1 + r/n)^(nt)

put the values in formula

CI = 30,000 ( 1 + 0.1/1)^(5)(1)

= 30,000 (1.01)^5

CI = 30,300^5

CI = \$31,530 Ans.

What is Simple Interest?

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### 1 Response

1. March 16, 2022

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