Simple Interest is the extra amount of money paid or earned on a principal amount after a certain period of time. It is calculated only on the original amount borrowed or invested throughout the entire period.
Unlike Compound Interest, Simple Interest does not earn interest on previously accumulated interest. The interest remains constant throughout the investment or loan period.
The Principal is the original amount of money that is borrowed or invested before any interest is added.
If Mary borrows $5,000 from a bank, then:
Principal (P) = $5,000
The Interest is the extra money paid by the borrower or earned by the investor for using money over a given period of time.
If a loan of $2,000 earns $300 after one year, then:
Interest (I) = $300
The Rate is the percentage of the principal charged or earned as interest per year.
It is usually written as a percentage (%).
If a bank charges 8% interest every year, then:
Rate (R) = 8% per annum (8% p.a.)
The Time is the period or duration for which the money is borrowed or invested.
Time is usually measured in years. If the time is given in months, convert it into years before using the formula.
If money is borrowed for 18 months, then:
18 months = 18 ÷ 12 = 1.5 years
The formula for calculating Simple Interest is:
Where:
The total amount after interest has been added is given by:
A = P + I
Where:
The final amount is obtained by adding the Simple Interest to the Principal.
Amount = Principal + Interest
Principal = $4,000
Interest = $800
Amount = Principal + Interest
Amount = 4,000 + 800
Amount = $4,800
Calculate the Simple Interest and the Total Amount on a principal of $8,000 invested at 6% per annum for 4 years.
Solution
Step 1: Write down the given information.
Principal (P) = $8,000
Rate (R) = 6%
Time (T) = 4 years
This identifies all the values needed for the formula.
Step 2: Write the Simple Interest formula.
I = P × R × T 100Step 3: Substitute the values into the formula.
I = $8,000 × 6% × 4 100 %The given values are now substituted correctly.
Step 4: Simplify.
I = $192,000 100I = $1,920
This is the Simple Interest earned.
Step 5: Find the Total Amount.
A = P + I
A = $8000 + $1920
A = $9,920
The total amount is obtained by adding the interest to the principal.
Final Answers
Simple Interest = $1,920
Total Amount = $9,920
A student borrowed $12,500 from a financial institution at 8% per annum for 3 years. Calculate the Simple Interest and the Total Amount payable.
Solution
Step 1: Identify the given values.
P = $12,500
R = 8%
T = 3 years
These are the quantities needed for the calculation.
Step 2: Write the formula.
I = P × R × T 100This formula calculates the interest earned.
Step 3: Substitute the values.
I = $12,500 × 8% × 3 100 %The values are substituted directly into the formula.
Step 4: Simplify.
I = $300,000 100I = $3,000
This is the interest payable.
Step 5: Calculate the Total Amount.
A = P + I
A = $12500 + $3000
A = $15,500
The amount is the sum of the principal and interest.
Final Answers
Simple Interest = $3,000
Total Amount = $15,500
Find the annual rate of Simple Interest if a principal of $6,000 earns $1,080 in 3 years.
Solution
Step 1: Identify the given values.
P = $6,000
I = $1,080
T = 3 years
We are required to find the rate.
Step 2: Write the Simple Interest formula.
I = P × R × T 100Step 3: Rearrange the Simple Interest formula by making rate the subject of the formula.
R = 100% × I P × TThis formula makes the rate the subject.
Step 4: Substitute the values.
R = 100% × $1,080 $6,000 × 3The known values are substituted correctly.
Step 5: Simplify.
R = 108,000 % 18,000R = 6%
This is the annual rate of interest.
Final Answer
Rate = 6% per annum
How long will it take for $5,000 to earn a Simple Interest of $900 at an annual rate of 6%?
Solution
Step 1: Identify the given values.
P = $5,000
I = $900
R = 6%
The unknown quantity is time.
Step 2: Write the Simple Interest formula.
I = P × R × T 100Step 3: Rearrange the Simple Interest formula by making Time the subject of the formula.
T = 100% × I P × RThis formula makes time the subject.
Step 4: Substitute the values.
T = 100% × $900 $5,000 × 6%The known values are substituted correctly.
Step 5: Simplify.
T = 90,000 30,000T = 3 Years
This is the required time.
Final Answer
Time = 3 years
Question
Determine the principal that will earn a Simple Interest of $2,400 in 5 years at an annual rate of 8%.
Solution
Step 1: Identify the given values.
I = $2,400
R = 8%
T = 5 years
The unknown quantity is the principal.
Step 2: Write the Simple Interest formula.
I = P × R × T 100Step 3: Rearrange the Simple Interest formula by making Principal the subject of the formula.
P = 100% × I T × RThis formula makes Principal the subject.
Step 4: Substitute the values.
P = 100% × $2,400 5 × 8%The known values are substituted correctly.
Step 5: Simplify.
P = $240,000 40P = $6,000
This is the original amount invested or borrowed.
Final Answer
Principal = $6,000
Attempt the following Questions:
(i) A farmer takes a loan of $4,000 from a local cooperative bank to purchase fertilizer. If the bank charges a simple interest rate of 6% per year, calculate the total interest the farmer will owe after 3 years.
(ii) Mary invests $7,500 into a fixed savings account that earns a simple interest rate of 4% annually. Find the total amount of money (principal plus interest) that will be in her account at the end of 5 years.
(iii) John borrowed $2,500 from a friend to repair his motorcycle and agreed to pay back a total of $300 in simple interest. If the agreed annual interest rate was 8%, calculate how long, in years, John kept the money.
(iv) An investor deposited $12,000 into a commercial venture. After exactly 2 years, the investment yielded a simple interest amount of $1,680. Determine the annual rate of interest that was applied to this investment.
(v) A student opens a savings account with a principal deposit of $1,500. The account pays an annual simple interest rate of 3.5%. How much total simple interest will the student earn over a period of 4 years?
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