Compound Interest: The Mathematics of Growth
by Yuvi K - December 16, 2023
What is compound interest (घटकी)?
Compound interest (घटकी) is the interest calculated not just on the initial amount of money invested (also known as principle investment (निवेश प्रथा) but also on the accumulated interest of past periods. It is the effect of interest earned over a period of time, much like an investment snowballing into a larger sum of money. Compound interest can be applied to all financial assets, such as stock portfolios, mutual funds, real estate, bank deposits, or any other investments.
How does Compound Interest work?
Compound interest works by taking the interest that is earned during each period, and adding that additional amount to the original principle amount. Therefore, the interest earned in the compound interest period is calculated not only from the original principle amount, but also from the accumulated interest of the past periods.
For example, if you have invested $200 with a 10% annual interest rate and the investment period is 5 years, at the end of year 5 you will have accumulated $329.71. This is the compound interest calculation.
The formula for compound interest calculation is as follows:
Final Amount = Principal Amount * (1 + Interest Rate)Time Period
In this example the final amount of $329.71 is calculated using the following formula:
Final Amount = 200 * (1 + 0.10)5 = 200 * 1.61051 = 329.71
When Does Compound Interest Become Useful?
Compound interest is most beneficial when a large sum of money is generated over a long period of time. This is because the longer the time period is, the more the interest accumulates and compounds. Consequently, the amount of interest grows exponentially.
In our example, if the principal amount of $200 is left to compound over 50 years, the final amount will be much higher than the principal. That is:
Final Amount = 200 * (1 + 0.10)50 = 200 * 5.59961 = 1119.92
Therefore, you will have accumulated $1119.92 from a principal of only $200 in 50 years. This is an important aspect of compound interest and it is known as the power of compounding.
Compounding Frequency
Compounding frequency is another aspect to consider when determining the effectiveness of the compound interest. Compounding frequency refers to the number of times in a period that interest will be added to the principal amount in a compound interest period.
For example, if the compounding frequency is monthly, then interest will be added 12 times over a year. Therefore, the higher the compounding frequency, the more effective the compound interest will be. In the example above, if the compounding frequency is changed to monthly, then the final amount would be much larger. That is:
Final Amount = 200 * (1 + 0.10/12)50*12 = 200 * 11.56648 = 2313.30
The effect of changing the compounding frequency to monthly has caused the final amount to grow from $1119.92 to $2313.30. This is due to the effect of compound interest compounding more frequently and thus, more quickly than before.
Compound Interest Calculators
Compound interest calculators make it easy to calculate the final amount of an investment over a period of time. You simply need to enter the principal amount, interest rate, and the period of time that the investment will remain untouched, and the calculator will generate an estimated final amount.
For example, if you enter the following inputs in a compound interest calculator:
– Principal Amount: \$200
– Interest Rate: 10%
– Compounding Frequency: Annual
– Investment Period: 10 years
The calculator will generate a final amount of: \$404.90.
This is the estimated final amount of the investment, given the values of the principal, interest rate, and period of time for the investment.
Conclusion:
Compound interest is an important concept when it comes to investing as it can result in substantial growth over a period of time. Compound interest can be used to generate a large sum of money over a long period of time, given the correct conditions. Calculators can be used to quickly and easily calculate the expected final amount of an investment. Compounding the interest rate more frequently will also result in greater growth in the final amount. Therefore, understanding compound interest can help anyone understand the power of investing and the potential for growth.
