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.
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. |
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.
FAQ
Which is better: compound interest or simple interest?
It depends on whether you’re saving or borrowing. Compound interest is great for savings accounts or when repaying a loan. But if you’re borrowing money, simple interest will cost you less.
What is the difference between simple and compound interest?
Simple interest is calculated just on the principal amount. In contrast, compound interest covers both the principal and the accumulated interest. This means compound interest grows faster because it earns interest on the interest you’ve already made.
Do banks use SI or CI?
Banks usually use compound interest for savings and investments and simple interest for loans.
I’m Archana R. Chettiar, an experienced content creator with
an affinity for writing on personal finance and other financial content. I
love to write on equity investing, retirement, managing money, and more.
