SIMPLE INTEREST

      Have you ever borrowed money from a friend or saved some cash at the bank? If so, you've already had a little taste of how interest works even if you didn't realize it.

        Let's say you borrow money from someone and agree to pay them a little extra as "thank you" for letting you use it or imagine the bank giving you a small reward just to keep your money there. That extra amount is called interest and one of the simplest ways to calculate it is through something called simple interest.

       Simple interest is all about finding how much extra money you earn or owe, based only on the starting amount or the principal, the interest rate, and the time involved. It's easy to learn, super useful in real life and can help you make smarter choices with your money.

        And now, introducing to you, Simple Interest

What is "Simple Interest"?

                   Simple interest is a type of interest that is always calculated based on the original amount of money (called the principal). The interest rate stays the same for each time period. For example, when you put money in a bank, the bank gives you extra money (interest) in return. There are different ways banks give interest, an done common way is through simple interest.

Before we talked more about simple interest, let’s first understand what a loan is.

                A loan is money that someone borrows from a bank or a lender to pay for things they need, like a house, car, education, or personal needs. Loans must be paid back over time, and usually with extra money added — this extra is the interest on the loan.

Simple Interest Formula

                    Simple interest is calculated with the following formula: I = P × r × t , where

            P  =  Principal

            r   =  Rate of Interest in % per annum

            t   =  Time, usually calculated as the number of years

*The rate of interest is in percentage r% (and is to be written as the quotient of r/100). If the rate of interest is 39% then r can be written as 39/100 = 0.39

✅  Principal: The principal is the amount that was initially borrowed (loan) or invested. The principal is denoted by P

✅   Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 63%, or 28.9%, etc. The rate of interest is denoted by r

✅   Time: Time is the duration for which the principal amount is given to someone. The time is denoted by t

✅    Interest: Interest owed or earned after t years. The interest, specifically simple interest is denoted by I

We can use this triangle image in getting formulas that can further solve the other variable, P, r, or t.

Simple Interest (I):  I  =  P × r × t 

Principal (P):   P  =  I / r × t 

Rate (r):   r  =  I / P × t 

Time (t):   t  =  I / P × r 

Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called the "Amount."

                                           Amount  =  Principal + Simple Interest     

or

        A  =  P + I

        A  =  P + (P × r × t)

        A  =  P × (1 + r × t)

Below are some example to better understand the process in getting the simple interest.

Example 1. Jaime's mother borrowed personal loan of PHP 1,000 from the bank and the rate of interest was 5%. What would the simple interest be if the amount is borrowed for 1 year?

    Given: 

        P  =  1,000

        r   =  5% = 5/100 = 0.05

        t   =  1

    Unknown:

        Simple Interest (I)

    Formula: 

        I  =  P × r × t 

    Solution:

        I  =  1,000 × 0.05 × 1

        I  =  50

  Therefore, the simple interest of the borrowed personal loan of Jaime's mother is PHP 50.   

Example 2. Adam borrows PHP 6,600 from his friend at 1.5% in simple interest and he promises to pay it back in 3 years. How much interest does he pay?

    Given:

        P  =  6,600

        r   =  1.5% = 1.5/100 = 0.015

        t   =  3

    Unknown: 

        Simple Interest (I)

    Formula:

        I  =  P × r × t

    Solution:

        I  =  6,600 × 0.015 × 3

        I  =  297

   Therefore, the interest Adam pay is PHP 297.  

Example 3. The interest earned at 2% is PHP 320 for 2 years. What is the principal?

    Given:

        r   =  2% = 2/100 = 0.02

        t   =  2

        I   =  320

    Unknown:

        Principal (P)

    Formula:

        P  =  I / r × t

    Solution:

        P  =  320 / (0.02 × 2)

            =  320 / 0.04

        P  =  8,000

   Therefore, the principal is PHP 8,000   

Example 4. A nurse put PHP 22,000 in the bank 15 years ago. She has earned PHP 21,450 in interest, nearly as much as her initial investment. What was rhe interest rate that the bank wa spaying her?

    Given:

        P  =  22,000

        I   =  21,450

        t   =  15

    Unknown:

        Rate (r)

    Formula:

        r   =  I / P × t

    Solution:

        r   =  21,450 / (22,000 × 15)

            =  21,450 / 330,000

        r   =  0.065

        r   =  0.065 × 100  =  6.5%

   Therefore, the nurse invested at 6.5% interest.  

Example 5. If you deposit PHP 500 at a simple interest rate of 4% for 2 years, what will be the total amount in your account after 2 years?

    Given:

        P  =  500

        r   =  4% = 4/100 = 0.04

        t   =  2

    Unknown:

        Amount (A)

    Formula:

        A  =  P + (P × r × t)

    Solution:

        A  =  500 + (500 × 0.04 × 2)

            =  500 + 40

        A  =  540

   Therefore, the total amount in your account after 2 years is PHP 540.   

Example 6. Elsa's father invest PHP 5,000 at a simple interest rate of 4% and she want to know how long it will take for the interest to reach PHP 1,000.

    Given:

        P  =  5,000

        r   =  4% = 4/100 = 0.04

        I   =  1,000

    Unknown:

        Time (t)

    Formula:

        t   =  I / P × r

    Solution:

        t   =  1,000 / (5,000 × 0.04)

            =  1,000 / 200

        t   =  5

   Therefore, it will take 5 years for the Elsa's father investment to earn PHP 1,000 in simple interest.   

REFLECTION

    Learning about simple interest isn't only about enhancing our skills to solve mathematical problem but also helps us understand how money works in real world. 

    It is important for us to learn how interest works as it teaches us to have a smart decision when it comes to money.  For example, you decided to have a saving account in a bank. You will first make sure to choose the right bank for you by looking at the interest rate given a period of time. Making sure that your money will be safe and will grow in time.

    In short, simple interest is not just a topic in mathematics, it is a tool or way that can empower us to make better choices with borrowing, saving, and investing money. It will make us informed and confident with our financial decisions. A skill that is important no matter what career we take.