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 1000 dollars from the bank for a year and the bank told Bill that they will charge 10% interest on the loan. It means that Bill will receive 1000 dollars from the bank but he needs to pay 10% interest when returning the loan. The 10% of 1000 dollars is 100 dollars. That 100 dollars is the "interest"(represented by "I") and 10% is the "interest rate"(represented by "r") but in slang, people still consider 10% as interest. It means that when Bill will return 1000 dollars to the bank, after a year, he also needs to pay the interest hence he needs to pay 1100 dollars to the bank. In that 1100 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 10% interest rate for a year, which means that if the number of years changes, so will the interest. At that time, Bill would pay 100 dollars after a year but now(since he is borrowing for two years), he needs to pay 200 dollars for two years. To calculate interest in an easy way, we have a formula that will calculate interest which is:

I = \frac {P \times r \times t}{ 100 } (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:

I = \frac {P \times r \times t}{ 1200 } (If time is expressed in months)

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

I = \frac {P \times r \times t}{ 36000 } (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 30,000 dollars at a simple interest rate of 6%.

P = 30,000 \qquad r = 6% \qquad t = 5 \quad years \qquad I = ?

Since the time is in years:

I = \frac {P \times r \times t}{ 100 }

I = \frac {30,000 \times 6 \times 5}{ 100 } = 9,000 dollars

 

Calculate the total amount paid in six months on a principal of 10,000 dollars at a simple interest rate of 3.5%.

P = 10,000 \qquad r = 3.5% \qquad t = 6 \quad months \qquad I = ?

Since the time is in months:

I = \frac {P \times r \times t}{ 1200 }

I = \frac {10,000 \times 3.5 \times 6}{ 1200 } = 175 dollars

Total amount = 10,000 + 175 = 10,175

 

How long will it take a principal of 25,000 dollars at a simple interest rate of 5% to become 30,000 dollars?

P = 25,000 \qquad r = 5% \qquad t = ? \quad years \qquad I = 30,000 - 25,000 = 5,000

Since the time is in years:

I = \frac {P \times r \times t}{ 100 }

And we need to find time then:

\frac { I\times 100 }{ P\times r } =t

t = \frac { 100 \times 5,000 }{ 25,000 \times 5 } = 4 years

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.