Mathematical Finance: Understanding Compound Interest

by Yuvi K - December 16, 2023

What is Mathematical Finance?

Mathematical finance is a field of applied mathematics that deals with the financial markets, instruments and equations used in quantitative analysis of financial decisions. It combines the practical elements of financial theory, such as derivative pricing, risk management, asset allocation, and pricing and hedging strategies, with the analytical skills of mathematical and statistical modelling and finance. Mathematical finance can be used to design models and techniques for decision making in the financial markets, such as portfolio management, hedging, derivatives trading, asset valuation and the calculation of expected option values.

Compound Interest:

Compound interest is a cornerstone of investment strategy, and it is essential to understand how compound interest works so you can identify and preserve your savings and investments over the long term. Compound interest (कॉम्पाउंड इंटरेस्ट) is interest that is returned with the principal amount plus the interest you have earned over a period of time. It is calculated using a mathematical formula, and the compound interest can be compounded at the end of each month, each quarter or each year.

The most important factor in determining the amount of compound interest earned is the rate of interest. The higher the rate of interest that is applied to the original deposit, the more compound interest can be earned. For example, if you deposit $500 with an interest rate of 10% p.a. and the interest is compounded annually, the amount of interest earned will be $50 (10% of $500). But if the interest is compounded monthly, the amount of interest earned will be $51.30 (10.26% of $500).

Compound Interest Formula

The formula for calculating compound interest is:

Compound Interest = Principal x (1 + Rate of Interest/Compounding Frequency)^{Compounding Frequency X Number of Years} – Principal

Where:

Principal is the initial amount of money invested.
Rate of interest is the actual rate applicable on the invested amount.
Compounding frequency defines the frequency at which interest is compounded.
Number of Years refers to the number of years the investment is held for.

For example, if a person invests $500 for three years at a rate of 10% p.a. and the interest is compounded annually, the amount of compound interest earned would be calculated as:

Compound Interest = 500 x (1 + 0.10/1)^{1 X 3}– 500

= 500 x (1.10³) – 500

= 500 x 1.331 – 500

= 166.50

This means that the total amount earned will be $666.50 (Principal amount + Compound Interest).

Compounding Frequency and Time Period

The compounding frequency and time period are two important factors that determine the amount of interest earned in compound interest. The compounding frequency refers to the time interval at which the interest is compounded, and the period of time for which the interest is calculated is called the time period.

The compounding frequency directly affects the amount of gain earned in compound interest. The more frequent the compounding is done, the more interest will be paid. For example, if the interest rate is 10% p.a. and the compounding is done quarterly, the rate will be 10/4 = 2.5% per quarter.

However, if the same investment is compounded monthly the rate of interest will be 10/12 = 0.83% per month, resulting in more interest being paid over the same time period.

Advantages of Compound Interest

Compound Interest provides many advantages for investment portfolio management. First, it helps create wealth even when there is no additional contribution to the principal amount. The interest earned is added to the account balance, and then that amount is used to generate more interest. This helps you save more money in the long run, compared to investing in regular interest (नियमित ब्याज).

Secondly, it encourages you to save more money in the future. Knowing that you can earn even more interest on the money you have already saved encourages you to contribute more to your savings account. Additionally, compound interest can also help you in creating an retirement income, as it allows you to grow your savings more quickly and efficiently.

Conclusion

Compound interest is a powerful tool for building wealth and creating a secure retirement income. Understanding how compound interest works and learning to maximize the potential of compound interest can help you to reach your financial goals. It is important to understand the rate of interest, the compounding frequency and time period to get maximum benefit from compound interest.