Understanding Compound Interest and Fixed Deposits

When you put money into a savings account or a fixed deposit (also known as a term deposit), the bank pays you for keeping your money with them. The reason your savings grow over time is mostly due to compound interest.

Compound interest is a process where the interest you earn starts earning its own interest. Unlike simple interest, which is only calculated on your original deposit, compound interest calculates returns on your starting balance plus any interest already added to the account. In this guide, we will explain how this math works, look at the historical background of the concept, and show you how to use the calculator above to plan your savings.

How the Process Works in a Bank

When you open a fixed deposit, the growth usually follows a set schedule:

• The First Cycle: During the first period, the bank pays interest based only on the money you deposited.
• The Next Cycles: In the following period, the bank calculates interest on your original deposit plus the interest you earned in the first cycle.
• The Long-Term Effect: Because your balance gets slightly bigger every cycle, the amount of interest you earn also increases. The longer you leave the money alone, the faster it grows.

The Math Behind the Calculator

The interactive tool at the top of this page uses the standard algebraic formula for compound interest. Here is what the formula looks like:

Here is a simple breakdown of what each letter means:

• P (Principal): Your starting investment.
• r (Annual Interest Rate): The yearly rate expressed as a decimal. If the bank offers 7%, you use 0.07 in the math.
• n (Compounding Frequency): How many times a year the bank adds interest to your balance. The calculator above lets you choose between Yearly (n=1), Half-Yearly (n=2), and Quarterly (n=4).
• t (Time): The number of years you plan to leave the money in the account.

Tracking the Growth Over Time

To really see how compound interest works, it helps to look at a long-term projection. The table below compares simple interest to compound interest on a $10,000 initial investment at an 8% annual rate.

Looking at a 20-Year Balance

When money is left to grow for decades, the interest earned can eventually become larger than the original deposit. The chart below shows an account left alone for 20 years at a 7.5% annual rate.

By the end of the 20-year period, most of the account balance is made up of interest rather than the initial deposit.

Using the Formula in Other Fields

The math behind compound interest is essentially the math of exponential growth. This means the same formula is used in several different fields outside of personal finance.

1. Business and Data Analysis

Financial analysts use a metric called Compound Annual Growth Rate (CAGR) to measure business revenue. Since a company's sales might go up 20% one year and down 5% the next, CAGR provides a single, smoothed-out average growth rate over a set period.

2. Biology and Population Studies

Scientists tracking the spread of a virus or the growth of bacteria use continuous compounding models. The math helps them predict future population numbers based on current growth rates.

Frequently Asked Questions (FAQ)