# Compound Interest : Definition, Difference between Compound & Simple Interest Rate.

Compound interest is very commonly using interest rate in case of borrowing and lending. Borrower and Investor is concerned about the interest rate and its compounding with the principal. Borrower usually tries to avoid this situation because for compound interest the borrower pay excessive interest payments. On the other-hand an investor prefer compound interest rate because compound interest increases the money of of an investor.

This articles may help to borrowers as well as investors to understand regarding the compound interest rate and its uses, calculation formula, advantages, and disadvantages, etc.

## Definition

Compound interest is the interest which is applied on the principal amount as well as on the accumulated interest. In compound Interest the principal amount not remain same because accumulated interest always added with the principal and makes a new principal.

This situation usually happens when a borrower fails to pay the installments as instructed in the loan agreement, or when an investor makes a fixed deposit for particulars periods of time. Compound interest increases the principal amount as well as interest amount of a person.

The loan interest usually calculated annually, semi-annually or quarterly and compound interest is applied accordingly. But most commonly, this is applied on an annual basis. Lenders add interest amount with the principal amount and charges interest on the total amount (Principal + Interest).

In Compound Interest the accumulated interest is added to the principal sum to calculate interest Point to be noted that if you are a borrower and trying to avoid the hassle of compound interest charging, you have to repay the loan installments in due time.

## Examples

Example 1: XYZ Ltd, borrowed \$ 1 million for 5 years and the interest rate for this borrowing is 5%. The installment size (simple) for this loan was \$250,000 p.a. But for the sudden drop of sales and for severe fund constraints, XYZ Ltd failed to pay any installments of this loan. Now you are requested to calculate the total interest using Compound Interest rate.

Solution:

 Year Principal Calculation Interest Amount Principal + Interest 1 10,00,000 10,00,000 * 5% 50,000 10,50,000 2 10,50,000 10,50,000 * 5% 52,500 11,02,500 3 11,02,500 11,02,500 * 5% 55,125 11,57,625 4 11,57,625 11,57,625 * 5% 57,881 12,15,502 5 12,15,502 12,15,502 * 5% 60,775 12,76,277

Total Interest Accumulated in 5 years = \$276,277

Principal plus Interest = \$10,00,000+276,277 = \$12,76,277

## Formula

To calculate compound interest following formula could be used :

A = P (1 + r/n) (nt)

Where,

A = The future value of the investment or loan, including the interest amount

P = The principal amount of the investment or the loan

r = Rate of interest (annual)

n = the number of times the interest are compounded in a year

t = duration of the investment or the loan

Now we will apply the above mentioned formula in the following example:

Mr. Butler deposited \$150,000 in a bank for the period of 6 years. The rate of interest are 4.3% and compounded quarterly. What is the balance after 6 years?

Using the above mentioned formula we will calculate the compound interest.

Here,

P = \$ 1,500

R = 4.3%

n = 4

t = 6 years

Therefor, the compound interest will be for 6 years is :

A = 1500 (1+.043/4) 4*6 = \$ 1,938.84

So, the balance after 6 years is 1,938.84.

## Difference between Simple Interest and Compound Interest

The major differences between Simple Interest and Compound Interest are presented in the following table:

 Subject Simple Interest Compound Interest Definition Simple interest is the interest which is charged on Principal amount Compound interest is the interest which is charged on Principal as well as accumulated interest Rate of Interest Interest rate is comparatively lower than compound interest rate Interest rate is comparatively higher than simple interest rate. Changing Principal Principal amount remains same at all the times Principal changed after adding accumulated interest amount. Here, Principal = Original Invested amount plus accumulated interest. Formula Simple Interest = P*r*n Compound Interest, A = P (1 + r/n) (nt)

## Conclusion

Both Simple and Compound interest rate are commonly using in investing and borrowing of finance. Most often, Investors prefer compound interest as this interest rate increases their principal amount. At the same time borrower would like to avoid compound interest rate because it make the borrower to pay excessive interest amount.