## Introduction

Calculus is the tough subject in high school and college that you never thought you would ever use again in real life. In reality, if you ever plan to have a credit card and wonder how to calculate your minimum payment, you should have paid attention in class. Credit card companies use calculus on certain aspects of your account every month.

## What is Calculus?

In Latin, calculus means stone. Stones were used in ancient Rome to count and perform arithmetic. To be technical, we can say that calculus is just another form of counting. It is more advanced than algebra or geometry and is used to solve complex problems. Isaac Newton and Wilhelm Leibriz developed what we know as calculus in the 1680's. Although Isaac Newton is mostly noted for the discovery, Leibriz published reports on it 20 years before Newton did. The main function of calculus is to calculate change, simultaneously working computations on continuously evolving problems. Differential and integral calculus are the two branches of calculus. Used to solved the curve's derivative (slope and steepness) is differential calculus, or differentiation. This is useful for calculating the speed of a rollercoaster. Integral calculus, also known as integration, is used for more complex figures. Areas and volumes, such as the amount of water in a waddling pool, are topics handled by integration.

## How Credit Card Companies Use Calculus?

When minimum payments on a credit card needs to be computed, calculus is the method used. Credit card companies use the differential type of calculus to calculate this amount. There are several variables that go into the calculation because it is calculated by the amount of money that is due by a certain time (usually the due date that is listed on the bill). Add on to that the interest rate given and it becomes a complicated task. With all the changing parts, interest rates and available balances, the calculation has to be done simultaneously in order to provide the customer with an accurate minimum balance. The calculation that is used to determine the minimum payment starts with determining the interest that has accrued since the last payment, or over the month. To calculate the amount of interest, the following calculation is done: Accrued interest = Beginning balance * (interest rate/12) The 12 in the calculation represents the number of months in a year. So, if you have a beginning balance of 5,400 and an interest rate of 9.75%, the accrued interest for the month would be $43.88. Once that amount is calculated, then we can find out what the minimum payment is. After establishing the credit and signing up with the credit card company, a minimum monthly payment was set for what absolutely have to be paid on the card each month whether you used it that month or not. Most of the time, this amount is pretty small; $20 is what is usually set. The minimum payment that is on the credit card statement is calculated as such: =MAX(Minimum month payment, interest + minimum monthly payment) This means that if the interest accrued added to the minimum monthly payment is less that the set minimum monthly payment, then the largest amount must be paid. For instance, take the problem above. The minimum payment is $20 and the interest is $43.88; those two added together would be $63.88. Based on this problem, the minimum payment would be $63.88 because it is the larger amount.