Investing is an essential part of an individual’s financial journey and doing it wisely requires in-depth knowledge about investment and related concepts.
Among the many concepts that shape investment strategies, compound interest stands out as a powerful force in multiplying returns and building substantial wealth.
Compound interest is the interest calculated on the initial principal as well as on the accumulated interest from previous periods.
In simpler terms, it is fixed interest earned on interest, compounding over time to generate exponential growth in an investment.
In this article, we will discuss what is compound Interest, the formula for compound interest, the compounding period, etc.
Table of Contents
Formula for Compound Interest
The formula for compound interest is as follows:
A=P×(1+r/n)^nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit or loan amount)
r = the annual interest rate (in decimal)
n = the number of times that interest is compounded per unit
t = the time the money is invested/borrowed for, in years
Example:
Let’s consider an example to demonstrate the calculation of compound interest in Indian Rupees over a period of 10 years.
Suppose you invest Rs.10,000 (P) in a fixed deposit account with an annual interest rate of 5% (r), compounded quarterly (n = 4) for a duration of 10 years (t).
A = 10000 × (1 + 0.05/4)^(4×10)
A ≈ 10000 × 1.647009 ≈ Rs. 16470.09
So, the future value of the investment after 10 years would be approximately Rs. 16,470.09, including the compound interest.
Compounding Period
The compounding period refers to the frequency at which the interest on an investment or loan is calculated and added to the principal amount. It determines how often the interest is compounded within a specified time frame like monthly, quarterly, yearly, etc.
Compound Annual Growth Rate (CAGR)
Compound Annual Growth Rate (CAGR) is a measure used to determine the mean annual growth rate of an investment over a specified period of time, assuming that the investment has been compounding over that time period.
It provides a smoothed annual rate of growth and is useful for comparing the returns on different investments over equal time frames.
CAGR is calculated using the formula:
CAGR = (Ending Value / Beginning Value)^(1/n) – 1
Where:
- Ending Value is the value of the investment at the end of the period.
- The beginning Value is the initial value of the investment.
- n is the number of years in the investment period.
How to Calculate Compound Interest?
The following is an illustration that can give you an idea of how to calculate the compound Interest-
The table is the calculation of compound interest for 10 years, with an initial investment of Rs. 10,000, an annual interest rate of 5%, and compounding annually:
| Year | Beginning Balance | Interest Earned | Ending Balance |
| 1 | Rs. 10,000 | Rs. 500 | Rs. 10,500 |
| 2 | Rs. 10,500 | Rs. 525 | Rs. 11,025 |
| 3 | Rs. 11,025 | Rs. 551.25 | Rs. 11,576.25 |
| 4 | Rs. 11,576.25 | Rs. 578.81 | Rs. 12,155.06 |
| 5 | Rs. 12,155.06 | Rs. 607.75 | Rs. 12,762.81 |
| 6 | Rs. 12,762.81 | Rs. 638.14 | Rs. 13,400.95 |
| 7 | Rs. 13,400.95 | Rs. 670.05 | Rs. 14,071.00 |
| 8 | Rs. 14,071.00 | Rs. 703.55 | Rs. 14,774.55 |
| 9 | Rs. 14,774.55 | Rs. 738.73 | Rs. 15,513.28 |
| 10 | Rs. 15,513.28 | Rs. 775.66 | Rs. 16,288.94 |
How Compound Interest is different than Simple Interest?
The following are the differences between Simple Interest Rate and Compound Interest Rate-
| Compound Interest | Simple Interest |
| Interest is calculated on the initial principal amount as well as on the accumulated interest over time. | Interest is calculated only on the initial principal amount. |
| A = P(1 + r/n)^(nt) | A = P(1 + rt) |
| Time has a significant impact on the final amount that you’ll earn therefore, long-term investment is beneficial when it comes to compound interest like bonds, stocks, etc. | Simple Interest remains constant over time till the maturity |
| Higher interest earned due to compounding | Lower interest earned compared to compound interest |
| Time has a significant impact on the final amount that you’ll earn therefore, long-term investment is beneficial when it comes to compound interest like bonds, stocks, etc. | Time has a minimal impact on the final amount so short-term investments are good option here like Fixed Deposit |
FAQ
Compound interest is the interest calculated on both the initial principal and the accumulated interest from previous periods, resulting in exponential growth over time.
Compound interest includes interest calculated on both the principal and accumulated interest, while simple interest is calculated only on the principal amount.
Interest can be compounded annually, semi-annually, quarterly, monthly, or even continuously, depending on the terms of the investment or loan.
Annual compounding calculates interest once per year, while continuous compounding recalculates interest continuously as per the frequency mentioned in the terms document like monthly, quarterly, etc.
Compound interest requires time to grow significantly, so shorter investment periods may not yield substantial returns. Additionally, compounding can be negatively impacted by fees, taxes, and inflation.
I’m Shiv Kumar, a graduate with a passion for finance, marketing, and technology. My journey into finance started with a desire to understand money management and investing.
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