Simple Interest - Formulas

Simple interest is a basic concept in finance that helps calculate the extra money paid or earned when borrowing or lending a certain amount of money for a specific period. This post will provide an informative explanation of simple interest and present the relevant formulas.

Simple Interest - Formulas Table

Simple Interest - Formulas
Definitions
1. Principal: The money borrowed or lent out for a certain period is called the principal or the sum.
2. Interest: Extra money paid for using other's money is called interest.
Formula for Simple Interest
If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest.
Let Principal = P, Rate = R% per annum (p.a.), and Time = T years. Then Simple Interest = (P x R x T) / 100
Determining Principal, Rate, and Time
To find the principal (P): P = (100 x Simple Interest) / (R x T)
To find the rate (R): R = (100 x Simple Interest) / (P x T)
To find the time (T): T = (100 x Simple Interest) / (P x R)

Explanation with example for each formula

Definitions

  1. Principal: The amount of money borrowed or lent out for a specific period is known as the principal or the sum.

  2. Interest: The additional amount of money paid for using someone else's money is called interest.

Formula for Simple Interest

If the interest on a sum borrowed for a certain period is calculated uniformly, it is known as simple interest. The formula to calculate simple interest is as follows:

$ \text{{Simple Interest (S.I.)}} = \frac{{P \times R \times T}}{{100}} $

Where:

  • P represents the principal or sum borrowed.
  • R denotes the rate of interest per annum (p.a.).
  • T signifies the time period in years.

Example Calculation

Let's consider an example to illustrate the application of the simple interest formula.

Example: A person borrows $5000 at an annual interest rate of 8% for a duration of 3 years. Calculate the simple interest.

Solution: Using the formula mentioned above, we can calculate the simple interest as follows:

$ \text{Simple Interest} = \frac{{P \times R \times T}}{{100}} = \frac{{5000 \times 8 \times 3}}{{100}} = \frac{{1200}}{{100}} = $1200 $

Therefore, the simple interest on the borrowed amount of \$5000, at an annual interest rate of 8% for a period of 3 years, amounts to \$1200.

Determining Principal, Rate, and Time

In certain situations, it may be necessary to determine the principal, rate, or time based on the given simple interest. The formulas for calculating these variables are as follows:

  1. To find the principal (P):

$ P = \frac{{100 \times \text{{Simple Interest}}}}{{R \times T}} $

  1. To find the rate (R):

$ R = \frac{{100 \times \text{{Simple Interest}}}}{{P \times T}} $

  1. To find the time (T):

$ T = \frac{{100 \times \text{{Simple Interest}}}}{{P \times R}} $

These formulas can be utilized when any one of the principal, rate, or time is unknown but the simple interest is given.

Example Calculation (Determining Principal, Rate, and Time)

Let's consider an example to illustrate how to determine the principal, rate, or time using the given simple interest.

Example: The simple interest on a certain sum of money is $750. The rate of interest is 6% per annum, and the time period is 5 years. Calculate the principal.

Solution: Using the formula to determine the principal, we have:

$ P = \frac{{100 \times \text{{Simple Interest}}}}{{R \times T}} = \frac{{100 \times 750}}{{6 \times 5}} = \frac{{75000}}{{30}} = \$2500 $

Therefore, the principal amount is $2500.

Similarly, the formulas provided can be used to determine the rate or time when the respective variables are unknown.

These formulas and examples demonstrate the practical application of simple interest calculations. By utilizing these formulas, individuals can effectively determine the interest amount, as well as determine missing variables when provided with the simple interest value.