7.a 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.

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