# Compound Interest Formula

## Introduction

Despite their expected academicism and narrow specialization, mathematical sciences find their application in the everyday life of society. If one does not take into account the reasonably obvious calculation of discount interest in the store, determining the amount of tax to be paid, or studying the amount of gasoline that will be needed for the trip, then particular emphasis should be placed on the use of equations and formulas in the business environment. It is not surprising that for the management of an enterprise, the use of mathematics is natural: people in business are continually dealing with financial flows, investments, interest shares, and tax deductions, hence serious enterprise does not forget about hiring a reliable and competent accountant. This paper will discuss the formula for calculating compound interest, which is particularly relevant when investing in the business environment.

## Formula

The investment market has a wide range of different tools and algorithms to simplify control over business processes. If the approach is standard, the investor makes a profit, returns the amount of the investment and looks for new projects, or stays with the previous share (Hazell, 2019). However, there is a way to increase the percentage of payments for which the formula is fair to use: ## Variables

The equation may seem complicated at first glance, although, in fact, the variables included in it are clear. When it comes to investing in projects, the businessman deals with interest, the initial and final amount, and, indeed, the timing of investment. In this formula, the variable r is responsible for the interest rate, and n indicates how many times the interest was calculated for the period t. Finally, P shows the amount of initial financial investments issued by the investor.

## Equation Explaining

This equation’s primary purpose is to show how the final investment amount changes over a long period at a fixed interest rate. Thanks to the phenomenon of complicated interests expressed through the formula, savings grow like a snowball: “the concept of compound interest is that interest is added back to the principal sum so that interest is gained on that already-accumulated interest during the next compounding period” (Hazell, 2019, para. 3). In other words, interest is continually being added to the amount that tends to increase — when compared to simple interest technology, the benefit is tangible.

## Two Solutions

Due to the fact that the equation is inextricably linked with chronology, there are at least two ways to solve it – the selection of variables and analytically. In the first case, the investor knows the main economic indicators, then he or she can use them to calculate the final sum. For example, if person A invests \$100,000 in initial investments for 12 months with an interest rate of 10%, the formula will demonstrate cost the investment after three years to:  The second way is to make a table to determine the stepwise data on financial flows. To calculate specific values, a table is created, which shows the amount of initial investment, income for a certain period, and the amount of final investment. As expected, the final amount of one reporting period equals the initial amount of the second, which can be called reinvestment. Nevertheless, it is not difficult to notice that the analytical method allows to receive only primary data on profit, while the exact calculation will show a concrete number.

 # Start Profit (Start*10%) Final 1 \$100,000 \$10,000 \$110,000 2 \$110,000 \$11,000 \$121,000 3 \$121,000 \$12,100 \$133,100

## Formula Use

In practice, there is an infinite number of scenarios of how this formula can be used. While some businessmen turn to the expression only in order to assess the benefits of the bank offer, others analyze and find out which investment fund meets the businessman’s expectations. For example, businessman B decides to invest \$100.00 at 5% for two years to find out how much he will get in half the time.  It is not difficult to understand that the profitability of such an investment is extremely low. Investors should, therefore, choose a fund that will give them more loyal terms (“Compound interest calculator,” “n.d.”). For example, investor C already has an account where \$10,000 was invested, and in 18 months, it grew to \$12,000. The Fund proposes to the entrepreneur to change the tariff for the annual increase of interest, then the businessman may think about the interest rate that will suit them:   ## Conclusions

In conclusion, it should be noted that the compound interest model is a frequently used tool that allows controlling one’s income. As has been shown in this paper, although the formula is aimed at economists, it can be used by a person even without economic education to calculate the benefits of bank deposits. In fact, the compound interest effect applies not only to bank deposits but also to other investment instruments: for example, bond and share settlements. Frequent high interest capitalization allows entrepreneurs to build up savings efficiently and quickly, although, in practice, it is necessary to find a balance between the interest rate and the investment period. As can be seen from the formula, it includes known financial parameters, hence, the use should not cause any problems. In addition, it was demonstrated that a formula could be turned upside down to calculate individual indicators — for example, the interest rate.

## Reference

Compound interest calculator. (n.d.). Web.

Hazell, A. (2019). Compound interest formula with examples. Web.

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BusinessEssay. (2022) 'Compound Interest Formula'. 7 April.

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