Simple Interest
Introduction
Simple interest is a basic concept in commercial arithmetic used to calculate the interest earned or paid on a principal amount for a certain period of time at a specified rate of interest. It is called "simple" because the interest is calculated only on the original principal, not on the accumulated interest.
The formula for calculating simple interest is:
[ \text{Simple Interest} (SI) = \frac{P \times R \times T}{100} ]
Where:
- ( P ) = Principal amount (the initial sum of money)
- ( R ) = Rate of interest per annum (as a percentage)
- ( T ) = Time period for which the interest is calculated (in years)
The total amount to be paid or received at the end of the period can be calculated as:
[ \text{Total Amount} (A) = P + SI ]
Example 1: Calculating Simple Interest on a Loan
Problem
John borrows $1,000 from a bank at a rate of 5% per annum for 3 years. Calculate the simple interest and the total amount he has to pay at the end of 3 years.
Solution
Given:
- ( P = 1000 ) (Principal amount)
- ( R = 5 % ) (Rate of interest)
- ( T = 3 ) years (Time period)
Using the simple interest formula:
[ SI = \frac{1000 \times 5 \times 3}{100} ]
[ SI = \frac{15000}{100} = 150 ]
So, the simple interest for 3 years is $150.
The total amount to be paid at the end of 3 years:
[ A = P + SI = 1000 + 150 = 1150 ]
Explanation
In this example, John borrowed $1,000 at an interest rate of 5% per year for 3 years. The interest was calculated only on the original principal of $1,000, resulting in a total interest of $150. Therefore, the total amount to be repaid after 3 years is $1,150.
Example 2: Finding the Principal
Problem
Sarah wants to save money in a bank account that offers 4% simple interest per annum. If she wants to earn $200 in interest after 2 years, how much should she deposit?
Solution
Given:
- ( SI = 200 ) (Simple interest)
- ( R = 4 % ) (Rate of interest)
- ( T = 2 ) years (Time period)
We need to find the principal, ( P ), using the simple interest formula:
[ 200 = \frac{P \times 4 \times 2}{100} ]
[ 200 = \frac{8P}{100} ]
Multiplying both sides by 100 to clear the fraction:
[ 20000 = 8P ]
Dividing by 8:
[ P = \frac{20000}{8} = 2500 ]
So, Sarah should deposit $2,500 to earn $200 in interest after 2 years.
Explanation
In this case, we rearranged the simple interest formula to solve for the principal. Sarah needed a principal of $2,500 to earn $200 in interest.