December 1, 2020

Chapters

The simplest definition of interest is that it is the amount of money that is paid in addition to the amount borrowed. The total interest is directly proportional to the amount borrowed and the duration of the loan. This might be a little bit difficult to understand, let's take help from an example for more clarity. For example, Bill wants to borrow dollars from the bank for a year and the bank told Bill that they will charge interest on the loan. It means that Bill will receive dollars from the bank but he needs to pay interest when returning the loan. The of dollars is dollars. That dollars is the **"interest"**(represented by **"I"**) and is the **"interest rate"**(represented by **"r"**) but in slang, people still consider as interest. It means that when Bill will return dollars to the bank, after a year, he also needs to pay the interest hence he needs to pay dollars to the bank. In that dollars, Bill paid interest + the amount borrowed.

The amount borrowed is called the **principal**(represented by **"P"**). In conclusion, Bill paid interest + principal after a year to the bank. Since we talked about special words, there are special words for Bill and the bank as well. We will call Bill as the **Borrower **and the bank will be **Lender**. There is another problem, in this whole example, we consider the time period as one year, what if Bill wants to borrow for two years? The question is, will this affect interest? Yes, it will. The bank offered interest rate for a year, which means that if the number of years changes, so will the interest. At that time, Bill would pay dollars after a year but now(since he is borrowing for two years), he needs to pay dollars for two years. To calculate interest in an easy way, we have a formula that will calculate interest which is:

(If time is expressed in years)

Where:

Concept | Name | Symbol |
---|---|---|

Amount borrowed | Principal | P |

Loan duration | Time | t |

Interest rate | Rate | r |

Additional amount | Interest | I |

However, the above formula is specified for the interest calculated for years. Every bank has a different interest calculating system, some calculate it in years, while some in months, and you might be a bit surprised to know that some calculate it in days. Does that affect the above formula? Yes, it does but don't worry, if you want to calculate the interest in months then use the below formula:

(If time is expressed in months)

And if you want to calculate the interest in days then:

(If time is expressed in days)

## Examples

**Calculate the amount of simple interest that is paid over a period of five years on a principal of dollars at a simple interest rate of .**

Since the time is in years:

dollars

**Calculate the total amount paid in six months on a principal of dollars at a simple interest rate of .**

Since the time is in months:

dollars

Total amount =

**How long will it take a principal of dollars at a simple interest rate of to become dollars?**

Since the time is in years:

And we need to find time then:

years