When you borrow money from someone or a bank, you pay interest on the principal amount. Similarly, when you lend money to someone or a bank, you earn interest on the principal amount. Simple interest is the type of interest that is charged on the principal amount borrowed or lent, and it is calculated based on the principal amount, interest rate, and the time period of borrowing or lending.
Formula: The formula for simple interest is straightforward, and it is given as:
Simple Interest = (P * R * T) / 100
where, P = Principal amount R = Rate of interest T = Time period
Examples:
Suppose you borrow $10,000 at an interest rate of 5% per annum for a period of 3 years. The simple interest on this loan would be:
Simple Interest = (10,000 * 5 * 3) / 100 = $1,500
Therefore, you would have to pay $1,500 as interest on this loan over a period of 3 years.
Let’s say you lend $15,000 to someone at an interest rate of 8% per annum for a period of 2 years. The simple interest earned on this loan would be:
Simple Interest = (15,000 * 8 * 2) / 100 = $2,400
Therefore, you would earn $2,400 as interest on this loan over a period of 2 years.
Advantages:
Simple interest is easy to calculate, and the formula is simple.
It is useful in calculating interest on short-term loans.
It is less complicated than compound interest.
Disadvantages:
Simple interest does not take into account the effect of inflation.
It does not consider the compounding effect, which means you do not earn interest on interest.
It is not suitable for long-term investments as the interest earned may not be substantial.
Here are some examples of simple interest problems with solutions:
Example 1: Calculate the simple interest on a principal of $5,000 at a rate of 4% per annum for 3 years.
Solution: Given, Principal (P) = $5,000, Rate (R) = 4% per annum, Time (T) = 3 years Simple Interest (SI) = (P x R x T) / 100 = (5000 x 4 x 3) / 100 = $600 Therefore, the simple interest on $5,000 at a rate of 4% per annum for 3 years is $600.
Example 2: Find the amount obtained on a principal of $10,000 at a rate of 6% per annum for 2 years, when the interest is compounded annually.
Solution: Given, Principal (P) = $10,000, Rate (R) = 6% per annum, Time (T) = 2 years, Compounding Period (n) = 1 Amount (A) = P(1 + R/n)^(nT) = 10000(1 + 0.06/1)^(1 x 2) = $11,236 Therefore, the amount obtained on a principal of $10,000 at a rate of 6% per annum for 2 years, when the interest is compounded annually, is $11,236.
Example 3: If $2,000 is invested for 5 years at a simple interest rate of 8% per annum, what will be the total amount at the end of the period?
Solution: Given, Principal (P) = $2,000, Rate (R) = 8% per annum, Time (T) = 5 years Simple Interest (SI) = (P x R x T) / 100 = (2000 x 8 x 5) / 100 = $800 Amount (A) = P + SI = $2,000 + $800 = $2,800 Therefore, the total amount at the end of 5 years on an investment of $2,000 at a simple interest rate of 8% per annum is $2,800.
Example 4: If $5,000 is borrowed at a simple interest rate of 12% per annum for 3 years, what will be the total amount to be paid back at the end of the period?
Solution: Given, Principal (P) = $5,000, Rate (R) = 12% per annum, Time (T) = 3 years Simple Interest (SI) = (P x R x T) / 100 = (5000 x 12 x 3) / 100 = $1,800 Total amount to be paid back (A) = P + SI = $5,000 + $1,800 = $6,800 Therefore, the total amount to be paid back at the end of 3 years on a loan of $5,000 at a simple interest rate of 12% per annum is $6,800.
Example 5: Suppose you borrow $2,000 from a friend and agree to pay back the loan with 5% simple interest after 3 years. How much interest will you have to pay, and what will be the total amount you owe at the end of the loan term?
Solution: The formula for calculating simple interest is:
I = P * r * t
where I is the interest, P is the principal (or amount borrowed), r is the interest rate, and t is the time period in years.
Plugging in the given values, we get:
I = 2000 * 0.05 * 3 = $300
Therefore, the interest you will have to pay is $300.
To calculate the total amount owed at the end of the loan term, we add the interest to the principal:
Total amount owed = Principal + Interest = $2000 + $300 = $2300
Therefore, at the end of the 3-year loan term, you will owe your friend a total of $2300.
Simple interest is a useful tool for calculating interest on short-term loans, and it is easy to calculate. However, it may not be the best option for long-term investments or loans as it does not take into account the effect of inflation or compounding. It is essential to consider all the factors before choosing the type of interest for your investment or loan.
