Sensex Today ## Simple Interest vs. Compound Interest

Interest is the price of borrowing money, where the borrower pays a charge to the lender for the loan. The interest sometimes expressed as a percentage could be both simple or compounded. Simple interest is based on the principal amount of a loan or deposit.

Simple Interest and Compound Interest In contrast, compound interest is based on the principal amount and the interest that accumulates on it in each interval. Simple interest is calculated solely on the principal amount of a loan or deposit, so it’s simpler to determine than compound interest.

### KEY POINTS Simple Interest and Compound Interest

• Interest is the price of borrowing money, where the borrower pays a charge to the lender for the loan.
• Usually, simple interest paid or obtained over a certain interval is a fixed percentage of the principal amount that was borrowed or lent.
• Compound interest increases and is added to the accumulated interest of earlier durations, so debtors should pay interest on interest in addition to principal.

## Simple Interest

Simple interest is calculated using the following formula:

Simple Interest= P×R×N  where:  P=Principal amount  R=Annual interest rate  N=Time period of the loan, in years​

Usually, simple interest paid or obtained over a certain interval is a fixed share of the principal quantity that was borrowed or lent. For instance, say a student obtains a simple-interest loan to pay one yr of college tuition, which prices Rs 18,000, and the annual rate of interest on the loan is 6%. The student repays the loan over three years. The quantity of simple interest paid is:

Rs 18,000 × 0.06 × 3​ = Rs3,240

and the entire amount paid is : Rs 18,000 + Rs 3,240​ = Rs 21,240

## Compound Interest

Compound interest accrues and is added to the accumulated interest of earlier periods; it contains interest on interest, in different words. The system for compound interest is:

Compound Interest = P×(1+R)^T−P where: P=Principal amount R=Annual interest rate T=Number of years interest is applied​

## Simple Interest and Compound Interest

It’s calculated by multiplying the principal amount by one plus the annual rate of interest raised to the number of compound durations, after which minus the discount within the principal for that yr. With compound interest, borrowers must pay interest on the interest in addition to the principal.

## Simple Interest vs. Compound Interest Examples

Beneath are some examples of simple and compound interest to grasp them better.

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### Example 1

Suppose you place Rs 5,000 right into a one-year Fixed Deposit(FD) that pays simple interest at 3% each year. The interest you earn after one yr could be Rs 150 :

Rs 5,000×3%×1​ = 150

## Simple Interest and Compound Interest

### Example 2

Continuing with the above instance, suppose your Fixed Deposit is cashable at any time, with interest payable to you on a prorated basis. If you cash the FD after 4 months, how much would you earn in interest? You’d obtain Rs 50:

Rs 5,000 × 3% × (4/12 yrs) = Rs 50

### Example 3

Suppose Sam borrows Rs 500,000 for 3 years from his wealthy uncle, who agrees to charge Sam simple interest at 5% yearly. How much would Bob pay in interest expenses yearly, and what would his whole interest expenses be after three years? (Assume the principal amount stays the same all through the three years, i.e., the complete loan amount is repaid after three years.) Sam must pay Rs 25,000 in interest charges yearly:

​Rs500,000 × 5% × 1 = Rs 25000​

or

Rs75,000 in total interest charges after three years: (​Rs25,000×3​ = Rs 75000)

## Simple Interest and Compound Interest

### Example 4

Continuing with the above example, Sam needs to borrow an extra Rs500,000 for 3 years. Sadly, his wealthy uncle is out of cash. So, he takes a loan from the bank at an interest rate of 5% per yr compounded yearly, with the complete loan amount and interest payable after three years. What could be the entire interest paid by Sam?

Since compound interest is calculated on the principal and accumulated interest, here’s how it adds up:

After 12 months,

Interest Payable = Rs 25,000 (Rs500,000 (Loan Principal)×5%×1)

After 24 months,

Interest Payable= Rs26,250 (Rs 525,000 (Loan Principal + Year One Interest)×5%×1 )

After 36 months

Interest Payable=Rs 27,562.50 (Rs551,250( Loan Principal + Interest for Years One and Two)×5%×1)

Total Interest Payable After Three YearsRs 78,812.50 (Rs25,000 + Rs 26,250 + Rs27,562.50)​

## Simple Interest and Compound Interest

It can be determined using the compound interest formula from above:

Total Interest Payable After Three Years = Rs 78,812.50 (Rs 500,000 (Loan Principal)×(1+0.05)3 − Rs500,000​)

This example exhibits how the system for compound interest arises from paying interest on interest in addition to the principal.