Financial mathematics is a fascinating field that empowers individuals to navigate their finances effectively and build wealth. Various principles and mathematical concepts serve as valuable tools for understanding and managing your finances like banks, inflation, CAGR, etc.
One of the important concepts to hold the key to wealth creation using investment is compound interest. Often regarded as magical, compound interest has the potential to transform financial outcomes.
In this article, we will discuss what is Compound Interest, the Formula for Compound Interest, what the is Compound period, and much more.
What is Compound Interest?
Compound Interest is the interest calculated on the initial principal sum, as well as the accumulated interest from previous periods, which is added to the principal sum. In other words, you earn interest on interest along with the principle.
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
Compound Interest Example
Suppose you deposit Rs. 10,000 in a bank account that offers an annual interest rate of 8% compounded annually. Let’s calculate the value of this investment after 3 years.
Using the compound interest formula:
A=P×(1+r/100)^n
A≈Rs.12,597
So, the investment would grow to approximately Rs. 12,597 after 3 years with compound interest.
What is a Compounding Period?
A compounding period refers to the frequency at which interest is calculated and added to the principal amount in a compounding interest scenario. It represents the intervals over which interest accrues and is reinvested into the investment or loan.
Common compounding periods include annual, semi-annually, quarterly, monthly, and daily, depending on the terms of the financial instrument or agreement.
Most investments would have the option to choose between the frequency of your payments out of these annual is best as it allows you to invest the full amount from day 1 resulting in accumulation of more interest.
Other Compounding Interest Concepts
The following are some of the important concepts that can help understand the compounding Interest better-
Time Value of Money
Time Value of Money is a financial principle that states that money received today is worth more than the same amount received in the future, due to its potential earning capacity.
It forms the basis for various financial calculations, including present value, future value, annuities, and loan amortization.
In the context of compound interest, the Time Value of Money is highest when you make a payment annually towards your investment as the full amount has an opportunity to earn more interest during a full 12-month increase of a small amount earning small interest month by month.
Compound Annual Growth Rate (CAGR)
Compound Annual Growth Rate is a measure of the annual growth rate of an investment over a specified period, taking into account the effect of compounding.
It smooths out fluctuations and provides a single growth rate that represents the true value of the investment.
How to Calculate Compound Interest?
To calculate compound interest, follow these steps using an example:
Suppose you invest Rs. 1,00,000/- in a fixed deposit account with an annual interest rate of 5%, compounded quarterly (4 times a year), for 10 years, which is as follows-
| Year | Amount (Rs.) | Compound Interest (Rs.) |
| 1 | 1,05,116.25 | 5,116.25 |
| 2 | 1,10,462.23 | 10,462.23 |
| 3 | 1,16,042.79 | 16,042.79 |
| 4 | 1,21,863.36 | 21,863.36 |
| 5 | 1,27,929.29 | 27,929.29 |
| 6 | 1,34,246.93 | 34,246.93 |
| 7 | 1,40,822.83 | 40,822.83 |
| 8 | 1,47,664.99 | 47,664.99 |
| 9 | 1,54,781.18 | 54,781.18 |
| 10 | 1,62,179.17 | 62,179.17 |
Difference between Compound Interest vs Simple Interest
The following are the differences between Compound Interest and Simple Interest-
| Compound Interest | Simple Interest |
| In Compound Interest, the interest is calculated on the initial principal and also on the accumulated interest from previous periods | Interest is calculated only on the initial principal amount |
| Formula:- A = P(1 + r/n)^(nt) Principal (P), interest rate (r), number of times interest is compounded per period (n), number of periods (t). | Formula:- A = P(1 + r/n)^(nt) Principal (P), interest rate (r), number of times interest is compounded per period (n), number of time periods (t). |
| Increases exponentially over time due to interest being added to the principal and compounded. | Formula:- A = P(1 + r/t) Principal (P), interest rate (r), period (t). |
| It is commonly used for long-term investments like savings accounts, fixed deposits, and loans. | It is often used for short-term loans, simple financial calculations, and scenarios where compounding doesn’t apply. |
| More complex calculation due to the need to calculate compound periods and interest on interest. | Easier to calculate as interest is constant and not affected by previous periods’ interest. |
FAQ
Compound interest is the interest calculated on the initial principal as well as on the accumulated interest from previous periods allowing your investment to earn higher returns as compared to Simple Interest.
Compound interest takes into account the interest on the initial principal and on the interest accumulated over time, leading to exponential growth. Simple interest, on the other hand, only applies to the initial principal amount.
When compared, Compound Interest tends to pay you more as the entire amount in your account gets the interest whereas in Simple Interest only the amount you’ve invested will be calculated.
The principal amount, the annual interest rate, the frequency of compounding, and the duration for which the interest is compounded are the key factors affecting compound interest.
Yes, compound interest can work against you in the case of loans or credit cards where unpaid interest accumulates and gets added to the principal, leading to a higher debt amount over time.
