Compound Interest vs Simple Interest: What’s the Difference?

Introduction:

Two friends invested in two similar instruments, but one earned more than the other. This is a common situation, and one reason for it is the different methods of computing the interest rate. 

‘Stay invested for the long term to enjoy the fruits of compounding.’ Isn’t this the most common investment you receive when you pick the stock market as your investment avenue? Agreed that long-term investments provide good accumulated wealth. But what is compounding? Is it different from what bank deposits and loans are subjected to? Let’s understand right from the basics. 

Understanding simple interest vs compound interest helps you make informed financial decisions. Whether you’re taking a loan, investing, or saving, the type of interest applied significantly affects your total earnings or repayments.

What is interest?

Interest is the cost of borrowing money or the reward for lending it. When you borrow, banks charge interest on top of what you repay. They also pay interest on savings and investment accounts to attract deposits, which they lend out at higher rates. Simply put, interest is extra money paid on loans or earned on deposits, calculated as a percentage. 

If you borrow Rs. 10,000 at an interest rate of 12%, you must repay the principal amount (Rs. 10000) plus the interest amount of Rs. 1200 (10000*12)/100. Similarly, if Rs. 10000 were a bank deposit at the same simple interest rate, you would receive Rs. 1200 after a certain period.

There are two types of interest systems – simple and compound interest. Let’s understand the concept of simple vs. compound interest.

Simple Interest vs Compound Interest Explained:

The basic difference between simple interest and compound interest is as follows-

Parameter	Simple Interest (SI)	Compound Interest (CI)
Definition	Interest calculated only on the initial principal amount.	Interest is calculated on the principal plus any accumulated interest.
Formula	SI=P×r×twhere p is principal, r is interest rate, and t is tenure or number of years	CI= P[1+(r/n)]^nt] – Pwhere p is principal, r is the rate of interest, n is the frequency of compounding, t is tenure
Amount (A)	A=P+SI	A=P(1+nr​)^nt
Application	Short-term loans, simple savings accounts.	Long-term investments, savings accounts, loans.
Interest Calculation	Simple, straightforward; interest remains constant.	More complex; interest compounds over time.
Frequency	It can be quarterly or monthly as well. However, the annual rate is divided accordingly. For example, 12% p.a. becomes 1% per month or 3% per quarter.	Quarterly, monthly, daily, etc., based on the compounding frequency. The interest rate doesn’t get divided.
Effect of Time	Linear increase in interest.	Exponential increase due to compounding effect.

Simple Interest vs Compound Interest Formula

Mathematical Differences Between the Two

• Simple Interest Formula: SI = (P × R × T) / 100
• Compound Interest Formula: CI = P[(1 + R/n)^(nT)] – P

Formula Comparison with Variables Explained

• P: Principal amount
• R: Annual interest rate
• T: Time (years)
• n: Number of times interest is compounded per year (only for compound interest)

Difference Between Simple Interest and Compound Interest

Key Differences at a Glance

Mathematical Differences Between the Two

The primary difference between simple interest and compound interest lies in how the interest amount is calculated over time.

• Simple Interest Formula: SI = (P × R × T) / 100
  This formula calculates interest based solely on the original principal amount throughout the entire term.
• Compound Interest Formula: CI = P[(1 + R/n)^(nT)] – P
  This formula accounts for both the initial principal and the interest that accumulates over each compounding period, resulting in exponential growth.

Formula Comparison with Variables Explained

• P (Principal): The initial sum of money that is either invested or borrowed.
• R (Rate of Interest): The annual interest rate expressed as a percentage.
• T (Time): The duration for which the money is invested or borrowed, usually in years.
• n (Compounding Frequency): The number of times the interest is compounded per year. Common frequencies include:
  • Annually (n = 1)
  • Semi-annually (n = 2)
  • Quarterly (n = 4)
  • Monthly (n = 12)
  • Daily (n = 365)

Interpretation:

• In simple interest, interest does not change over time since it’s always calculated on the original principal.
• In compound interest, the effective base increases over time as interest gets added to the principal each compounding period, leading to faster growth.

Example Comparison:

• For a principal of ₹10,000 at 10% annual interest for 3 years:
  • Simple Interest = (10,000 × 10 × 3)/100 = ₹3,000
  • Compound Interest (annual compounding) = 10,000 × (1 + 0.10)^3 – 10,000 = ₹3,310

This additional ₹310 in compound interest arises because each year, interest is also earned on the previously accumulated interest.

When to Use Simple Interest vs Compound Interest

Scenarios Where Simple Interest is Applied

• Car loans
• Consumer loans
• Short-term deposits

Scenarios Where Compound Interest is Applied

• Fixed deposits
• Mutual funds
• Savings accounts

How Financial Institutions Use Each Type

Banks use compound interest to grow investments and often use simple interest when calculating loan repayments.

Pros and Cons of Simple and Compound Interest

Advantages and Disadvantages of Simple Interest

• Easier to calculate
• Lower total repayment for borrowers

• Doesn’t reward long-term investments
• Yields lower returns for savers

Advantages and Disadvantages of Compound Interest

• Offers higher returns over time
• Encourages long-term investing

• More complex to understand
• Can result in higher debt if used for borrowing

A] Simple Interest:

Simple interest is a direct method to calculate interest. It’s used mainly for short-term loans or investments. Simple interest only considers the initial amount of money invested (principal) to calculate annual interest. So, say the principal is Rs.10,000 and the interest is 10%; every year, the 10% interest will be computed on Rs.10,000 only. The interest is calculated as a percentage of the principal amount using this formula:

SI = PNR/100 

where P is principal, N is the number of years, and R is the interest rate.

For example, say you deposited Rs.50,000 at a simple interest rate of 10% for 2 years. At the end of the tenure, when you claim your deposit back, you will get the principal amount (Rs.50,000) plus the interest amount of Rs.10,000 [(50000*2*10)/100].

You’ll commonly see simple interest applied in car loans and consumer loans. Even certificates of deposit use simple interest to determine the returns on your investment. As a borrower, you benefit from simple interest because you don’t pay interest on accumulated interest. This keeps your overall payments lower compared to compound-interest loans. However, simple interest might yield lower returns if you’re an investor since your earnings don’t grow exponentially over time. 

B] Compound Interest:

Compound interest works differently from simple interest. Instead of just earning or paying interest on the principal amount, compound interest builds on both the principal and the already accumulated interest. This means your investment grows faster because you’re earning interest on interest. Over time, this leads to exponential growth.

The formula for calculating compound interest is-

CI = Principal × (1 + Rate/100)ⁿ − Principal

or

CI = Amount – Principal 

where Amount (A) =  Principal × (1 + Rate/100)ⁿ

If you’re borrowing money with compound interest, you’ll pay interest on the original amount and the already-added interest. On the other hand, if you’re saving or investing, the interest on your money will grow over time.

For instance, say you deposited Rs.1,00,000 for 3 years at 10% per annum. At the end of three years, you will get 

A= 100000 x (1+10/100)^3 = 1,33,100

Out of Rs.1,33,100, Rs.33,100 will be the compound interest

Interest can be compounded daily, monthly, quarterly, semiannually, or annually. The more frequently it’s compounded, the more you earn or pay. How? Let’s continue with the example where you deposited Rs.1,00,000 for three years. Annual compounding gave you Rs.133100, and ‘N’ in the formula was 3. So, 

• Quarterly compounding means compounded four times a year. Thus, N here will be 4×3. Consequently, the amount becomes approx Rs.1,34,489.
• Monthly compounding will result in N=36, and the amount you get after three years will be approx Rs.1,34,885. 

Simple Interest vs Compound Interest:

• Interest is charged differently depending on whether you use simple or compound interest. With simple interest, you’re only charged on the principal amount. But with compound interest, you’re charged on both the principal and any interest that has already accrued.
• Compound interest leads to faster growth because you’re earning interest on your interest. This causes exponential growth, unlike the steady, linear growth with simple interest.
• Because of this compounding effect, returns from compound interest tend to be higher over time than those from simple interest, given the same interest rate and investment period.
• Both types of interest calculations start with the principal amount. However, compound interest amplifies the effect of the principal due to the interest-on-interest effect.

How do both SI and CI work?

In terms of savings and investments, simple interest is commonly used in different types of accounts and securities. Here’s how it works with some examples:

• Certificate of Deposit (CD): If you invest Rs.1,000 in a five-year CD with a 4% simple interest rate, you’ll earn Rs.200 by the end of the term. If the interest compounded monthly, you’d earn Rs.221 instead.
• Dividend Reinvestment: Suppose you buy 100 company shares at Rs.2 per share, and you get Rs.200 in dividends. By reinvesting these dividends to buy more shares, your dividend payments will grow, allowing you to purchase even more shares over time.
• Buy-and-Hold Investing: Rs.500 monthly for 30 years with a 10% annual return could grow your portfolio to over Rs.1.1 million. You’d invest a total of Rs.1,80,000 over the 30 years.

Why the difference in returns? 

Say you invested Rs.1,00,000 for 10 years at 5% per annum. If it is simple interest, you can easily calculate 5% of the principal and multiply it by ten years, thus getting an amount of Rs.150000 after the tenure. In compound interest, the computation goes like this-

Year	Principal at Start	Interest for the Year	Total at Year-End
1	₹100,000	₹5,000	₹105,000
2	₹105,000	₹5,250	₹110,250
3	₹110,250	₹5,512.50	₹115,762.50
4	₹115,762.50	₹5,788.13	₹121,550.63
5	₹121,550.63	₹6,077.53	₹127,628.16
6	₹127,628.16	₹6,381.41	₹134,009.57
7	₹134,009.57	₹6,700.48	₹140,710.05
8	₹140,710.05	₹7,035.50	₹147,745.55
9	₹147,745.55	₹7,387.28	₹155,132.83
10	₹155,132.83	₹7,756.64	₹162,889.47

Here, instead of Rs.50000 interest, you get Rs.62,889.47 after 10 years. With CAGR, you can also calculate an estimated rate for each year in case of compound interest. How to calculate CAGR? The compounded Annual Growth Rate will tell you the average yearly growth rate over the period, thus helping you know how much your investment has grown each year. The formula used for this is-

CAGR = (FV / PV) ^ (1 / n) – 1, where FV is future value (the amount you got at the end of the tenure) and PV is present value (the amount you invested)

Conclusion:

When you’re thinking about where to park your savings or where to take a loan from, knowing the difference between interest types is crucial. A complete idea of simple interest vs compound interest definition will help you plan your loan repayments and investments in a better manner, thereby improving your financial standing in the longer run. However, when planning your next step, consider consulting the best share market advisory for informed decision-making and investing basis the stock intrinsic value.

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