Interest is simply the cost of borrowing, fees paid by the borrower to the lender for funds loaned to him. Interest is generally expressed as a percentage and can be either simple or compounded. One major difference between simple and compound interest is that simple interest is based on principal amount alone, whereas compound interest is based on principal amount along with interest compounded for a cycle of the period. Both simple and compound interest are important concepts used widely in financial services. Loans such as auto loans, educational loans, mortgages, or installment loans use simple interest.  The savings account uses the compound interest as it pays the interest on the sum deposited with it. Compound interest pays more than simple interest.

### SIMPLE INTEREST

Simple interest is a straightforward and easy way of calculating interest on a given sum of money. Simple interest paid or received is usually a fixed percentage of the principal amount borrowed or lent. Simple interest can be determined by multiplying the principal by the annual rate of interest by the number of years between the payments. The formula for simple interest can be written as follows:

SIMPLE INTEREST(SI) = (PXRXT)/100

Where, P = PRINCIPAL, R = RATE OF INTEREST, T = TIME(PERIOD)

The time is generally in years and rate of interest in percentage (%).

We can calculate the total amount using the following formula:

AMOUNT = PRINCIPAL + INTEREST

Where the amount is equal to the total amount paid at the end of the period.

Example: A student Ram obtains a student loan of Rs. 5 lakhs at an annual interest rate of 6%. He repays the loan after 5 years. The simple interest on this loan can be calculated as follows:

(5 lakhs X 6 X 5) /100 = 1.5 lakhs. Therefore, the total interest payable shall be Rs. 1.5 lakhs. The total amount to be repaid = 5 lakhs + 1.5 lakhs = Rs. 6.5 lakhs

### COMPOUND INTEREST

Compound interest is calculated on the principal amount and the interest accumulated over the previous period. It is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods, and then minus the principal amount to get the interest amount. The compound interest is added to the principal amount to calculate the interest of the next period. The formula for compound interest can be written as follows:

COMPOUND INTEREST (CI) = PRINCIPAL (1+RATE/100)n – PRINCIPAL

Where, P = PRINCIPAL, R = RATE OF INTEREST, T = TIME (PERIOD)

We can calculate the total amount using the following formula:

AMOUNT = PRINCIPAL (1+RATE/100)n= PRINCIPAL + INTEREST

Example: Mr. Shyam deposited Rs.2 lakhs with a bank at an annual interest rate of 6%. The deposit matures after 5 years, and interest is compounded annually. The compound interest on this deposit can be calculated as follows:

2 lakhs (1+6/100)5 – 2 lakhs = 67,645 (approx.). Therefore, the total interest receivable shall be Rs. 67,645 and the total amount = 2 lakhs + 67,645 = Rs. 2,67,645

### DIFFERENCE BETWEEN SIMPLE INTEREST AND COMPOUND INTEREST

The key difference between simple interest and compound interest can be understood with the help of the following points:

·   Simple interest is based on the principal amount alone whereas compound interest is based on the principal amount and interest that accumulates in every period.

·   The return amount will always be greater in the case of compound interest as compared to simple interest. (CI > SI)

·   The principal amount is constant in case of simple interest, whereas the principal keeps on varying during the entire borrowing period in case of compound interest.

·   The growth remains constant for simple interest methods, whereas the growth increases quite rapidly under compound interest methods.

·   Even if interest is paid annually, semi-annually, quarterly, or monthly, the total interest amount remains the same in the case of the simple interest method. But, in the case of the compound interest method interest amount increases as the period of compounding decreases, i.e., the interest that accrues on quarterly compounding will be greater than on annual compounding.

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