Difference Between Compound Interest and Simple Interest

Simple interest is dependent on the principal amount, which is the primary distinction between it and compound interest. Compound interest, on the other hand, is calculated using the principal amount plus interest compounded throughout the period.

The two key ideas of simple and compound interest are utilized extensively in a variety of financial services, particularly banking. Simple interest is used in loans, including mortgages, auto loans, school loans, and installment loans. Most savings accounts use compound interest since it covers the interest.

What is Simple Interest

Simple interest is a fixed rate of interest applied to the initial principal amount each time in a time cycle. Any bank that we invest money in will provide us with interest based on the amount we invested. It is one of the various forms of interest that banks apply.

A loan is a sum of money that someone borrows from a bank or other financial institution to meet their requirements. Examples include home loans, vehicle loans, school loans, and personal loans. The borrower must promptly return the loan amount to the authorities along with an additional sum, which is often the interest incurred on the loan.

Simple Interest Formula

The formula for calculating simple interest is S.I. = (P × R × T)/100, where P stands for principal, R for the rate of interest expressed as a percentage each year, and T for time, which is typically expressed as the number of years. The interest rate is expressed as a percentage, or R%. It should be stated as R/100 or 100 in the calculation.

Principal

The amount borrowed or invested is known as the principal. The letter "P" stands for it. In compound interest calculations, the principal increases with each cycle, whereas in simple interest calculations, it stays fixed.

Rate

The term "rate" refers to the interest rate at which the principal amount is borrowed or invested for a given length of time. For instance, the interest rate might be 10%, 14%, or 20%. In this case, "R" can stand for the interest rate.

Time

Time is the amount of time that the principal is invested or borrowed. "T" is the sign for time.

Amount

A person who obtains a bank loan is obliged to pay back the main amount borrowed plus interest; the entire sum paid back is known as the Amount. The letter "A" stands for it.

Principal + Simple Interest = Amount

A = P + S.I.

A = P + PRT

A = P (1 + RT)

How to Find Simple Interest

Step 1: Note the loan amount, principle (P), interest rate (R), and time (T).

Step 2: To compute simple interest, use the formula S.I. = (P×R×T/100).

Step 3: Replace all of the Step 1 values in Step 2 with the same values.

Step 4: To achieve the necessary simple interest, simplify the value that was obtained in Step 3.

Example of Simple Interest

Calculate the SI for 10,000 rupees deposited over 4 years at a rate of 10% per annum.

Solution:

Given,

P = 10,000 rupees

R = 10% per annum

T = 4 years

Thus, SI = (P×R×T/100)

⇒ SI = (10000×10×4)/100 = 4,000

Thus, the interest earned is rupees 4,000.

Applications of Simple Interest

Bank Loans: Many people in India obtain bank loans for various purposes, including financing schooling, purchasing a car, or buying a home. Usually, banks use simple interest to determine the interest on these loans. It is important for borrowers to know the amount of interest they will accrue during the loan.

Fixed Deposits: Banks offer interest to customers who place money into fixed deposits based on the principal amount placed. Simple interest is typically used to compute the interest earned. During the F.D. tenure, investors can calculate their returns using basic interest calculations.

Recurring Deposits: Recurring deposits (RDS), like fixed deposits, let people accumulate savings over time. Interest accrued on recurring deposits is likewise computed using simple interest. Clients can determine the final amount they'll receive at the conclusion of the R.D. period by considering the monthly deposit and the relevant interest rate.

Retail Installment Plans: Many retail establishments offer installment plans to customers who want to buy appliances, furniture, or electronics. Simple interest is frequently assessed on the installment payments under these programs. By computing the simple interest component, customers can determine the total amount they will pay during the installment period.

Microfinance: In India's small towns and rural areas, microfinance organizations offer financial assistance to low-income people and business owners who might not otherwise have access to regular banking options. Simple interest is commonly used to determine the interest rate on microloans. The principal borrowed plus the relevant interest rate will determine the total amount that borrowers must repay.

What is Compound Interest

Interest computed on both the principal and interest earned in the past is known as compound interest. The symbol for it is C.I. It is quite helpful for investing and loan repayment. "Interest on interest" is another name for it.

In addition to being helpful in other industries, compound interest is particularly helpful in the banking and financial sectors. Among the uses for it are:

• Population growth within a nation.
• The value of an investment over time.
• For determining any article's depreciated value and inflated costs.
• For forecasting the expansion of any nation or institution.

Formula of Compound Interest

After figuring out the entire amount over time using the starting principal and interest rate, compound interest is computed. The formula to calculate compound interest (CI) is as follows: with an initial principal of P, a rate of interest per annum of r, a period t in years, and a frequency of interest compounding frequency n, the formula is as follows:

CI = P (1 + r/100)n-P<

P = Principal

r = Rate of Interest

n = Number of Times Interest is Compounded Per Year

t = Time (in years)

A - P = compound interest.

Whereas

A = Total Money Amount Following Compounding

P stands for Principal Amount at First

How to Calculate Compound Interest

Interest paid on both principal and accrued interest is known as compound interest. The principal keeps growing because the interest collected at each interval is applied to the original amount.

To find compound interest, use the procedures listed below.

First Step: Note the Principal, Rate, and Time

Step 2: Use formula A = P (1 + r/100)n to calculate the amount.

Step 3: Apply the formula to find compound interest. Amount - Principal = CI

Applications of Compound Interest

Savings Accounts: Many savings accounts allow compound interest, which adds interest on a regular basis (typically monthly or quarterly) to the principal. Compared to simple interest, this causes savings to grow more quickly over time.

Investments: Compound returns are frequently produced by investment vehicles like mutual funds, stocks, and bonds. Reinvesting interest or dividends can intensify the compounding effect and result in a substantial buildup of wealth over time.

Mortgages And Loans: Interest is usually charged on loans and mortgages and added to the principal amount. This implies that borrowers pay interest on both the principal amount of the loan and the accrued interest.

Exponential Growth: Over a predetermined length of time, a population will grow at a pace proportionate to its current size. This phenomenon is known as exponential growth. This is comparable to compound interest, in which the population increases based on the number of new members recruited over time in addition to the starting population size.

Exponential Decay: Over a predetermined length of time, exponential decay is the rate at which a population declines relative to its current size. Compound interest and population reduction are comparable to this.

Difference Between Compound Interest and Simple Interest

Conclusion

Simple interest relies solely on the principal amount, while compound interest involves interest on both the principal and accumulated interest. Compound interest fosters exponential growth, making it beneficial for long-term investments. Understanding these differences is key to making informed financial decisions.