Simple Interest: Definition, Formula, Solved Examples, Facts

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What Is Simple Interest?

Simple interest is a straightforward method of calculating interest on a loan or deposit. It is based on the initial principal amount, and the interest remains constant throughout the entire term of the loan or investment. 

When borrowing money, the lender charges interest on the loan. When repaying the loan, the borrower must pay back the initial principal amount along with the interest accrued. The interest is calculated as a percentage of the initial principal, and it does not compound on any previously earned interest. 

Simple interest is commonly used for short-term loans, such as personal loans or short-term deposits, and is easy to understand and calculate, making it a popular choice for basic interest calculations. 

Simple interest meaning explained with an example:

Imagine you lend $\$1,000$ to your friend, and they agree to pay you back with a $5\%$ interest rate per year. How does simple interest work here? With simple interest, the interest remains the same every year, and it doesn’t “grow” over time. 

So, after one year, your friend owes you the original $\$1,000$ plus an additional $\$50$ in interest ($5\%$ of $\$1,000$). In the second year, they pay another $\$50$ as interest, and so on. The interest doesn’t compound or increase with time; it’s a fixed amount each year based on the initial $\$1,000$ borrowed. Now, let’s define simple interest.

Definition of Simple Interest

Simple interest is the interest earned on a principal amount, calculated at a specified interest rate and over a certain period. 

Simple Interest Formula

Simple interest is calculated by the following formula:

$S.I. = \frac{P \times R \times T}{100}$

OR

$S.I. = P \times r \times T \frac{R}{100} = r$

where,

P : Principal amount which is the initial amount borrowed or invested.

$\frac{R}{100} = r$ : Rate of interest 

T : Time refers to the duration for which the principal amount is lent or borrowed. It is usually expressed in years or months.

The amount is the money that an individual receives from the borrower, which is the total of principal and interest amount. It can be expressed as:

Amount $=$ Principal $+$ Simple Interest

$A = P + S.I.$

$A = P + \frac{P \times R \times T}{100}$

How to Find Simple Interest

Step 1: Identify the principal amount: Determine the initial amount borrowed or invested.

Step 2: Find the interest rate: Identify the interest rate specified as a percentage.

Step 3: Determine the time period: Note the length of time the money is borrowed or invested for.

Step 4: Calculate simple interest: Multiply the principal amount, interest rate (in decimal form), and time period together:

Step 5: Simple Interest $=$ Principal Amount $×$ Interest Rate (as decimal) $×$ Time Period

The result is the simple interest earned or paid on the principal amount.

Example: John borrowed $\$2000$ from a bank at the rate of interest of $10\%$ p.a. What will be the simple interest if it is borrowed for 5 years?

Principal amount $= \$2000$

Rate of interest $= 10\% = \frac{10}{100} = 0.10$

Time $= 5$ years 

$S.I. = \frac{2000 \times 10 \times 5}{100}$

$S.I.= \$1000$

Simple Interest vs. Compound Interest

Simple interest and compound interest are interest calculating methods used widely in banking and financial organizations. In simple interest, the principal amount is the same every year, while in compound interest, the amount at the end of one year is the principal amount for the next year. Let us explore more differences between simple interest and compound interest.

Simple InterestCompound Interest
It is calculated only on the initial principal amount.It is the interest calculated on the total accumulation of principal and interest amount.
Simple interest formula $= P \times r \times T$
$S.I. = \frac{P \times R \times T}{100}$                      where $r = \frac{R}{100}$
Compound interest formula =  $P(\frac{1 + r}{n})^{nt}-P$
The interest is the same for every year on the initial principal amount.The interest is different for every time period, as it is calculated upon the accumulated amount, not the initial principal.
Its growth over the period of time is uniform.Its growth has increased rapidly.
Often used for short-term loans and depositsCommonly found in long-term investments like savings accounts or loans

Facts about Simple Interest

  • Simple interest is the fundamental for interest calculation from which other interests like compound interest are derived.
  • The amount received from simple interest is comparatively lesser than the amount received by compound interest.
  • In simple interest, the principal amount is the same every year. 
  • The interest earned or paid with simple interest is proportional to the principal amount and the time period, without any additional factors.

Conclusion

In this article, we learned about the concept of simple interest and how it is calculated using the principal amount, interest rate, and time period. Simple interest provides a straightforward method to determine the interest accrued on a loan or investment. To reinforce our understanding, let’s now apply the simple interest formula through solving examples and attempting MCQs for better comprehension.

Solved Examples of Simple Interest

1. What is the simple interest if the principal is $\$1000$ invested for 10 years at the interest rate of $5\%$ per annum? 

Solution: 

Principal $= \$1,000$

Rate of interest $= 5\%$

Time $= 10$ years

By using simple interest formula,

$S.I. = \frac{P \times R \times T}{100}$

$S.I. = \frac{1000 \times 5 \times 10}{100}$

$S.I. = \$5,000$

Therefore, the simple interest $= \$5,000$

2. How much did Mary invest at $10\%$ annual simple interest for 5 years to earn $\$2000$?

Solution:

Rate of interest (R) $= 10\% = 0.10$

Time (T) $= 4$ years

Amount (A) $= \$2,000$

Principal (P) $=$ ?

By using amount formula of simple interest,

$A = P (1 + RT)$

$2000 = P (1+ 0.10 \times 4)$

$2000 = P (1.4)$

Dividing both sides by P.

$P = 20001.4$

$P = \$1,428.5$

Thus, Mary invested $\$1,428.5$ as a principal amount.

3. Find the total amount received by Michael if he invested a principal amount of  $\$3000$ and receives $\$1500$ as interest.

Solution:

Simple interest $= 1500$

Principal amount $= 3000$

To calculate the total amount received,

Amount $=$ Principal $+$ Simple Interest

Amount $= 3000 + 1500$

Amount $= \$4500$

Practice Problems on Simple Interest

Frequently Asked Questions about Simple Interest

Yes, the formula for simple interest is consistent for all types of loans and investments. 

Simple Interest $=$ Principal $\times$ Rate $\times$ Time.

Yes, simple interest can be used for both loans and investments, as it calculates the interest earned or paid on the principal amount.

We can calculate the simple interest for monthly by dividing the yearly interest by 12. Thus, the formula for calculating simple interest monthly is expressed as: $SI = \frac{P \times R \times T}{100 \times 12}$

Yes, simple interest is easier to understand and calculate, making it advantageous for short-term loans with straightforward interest calculations.

The longer the time period, the higher the total simple interest amount, as the interest accumulates linearly over time.