Question

If the simple interest on a sum of money for 4 years at 8% per annum is Rs 1,920, find the principal.

• A. Rs 5,000
• B. Rs 6,000
• C. Rs 7,500
• D. Rs 8,000

Hint:

You can use effective percentage interest to solve this faster.
At 8% per annum for 4 years, the total simple interest accrued is $8\% \times 4 = 32\%$ of the principal.
We are given that $32\%$ of the Principal is equal to Rs 1,920.
So, $1\% = 1920 \div 32 = 60$.
The principal ($100\%$) is $60 \times 100 = 6000$ instantly.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question is based on the concept of Simple Interest in financial mathematics.
Simple interest is calculated on the initial principal amount and remains constant each year if the interest rate and principal do not change.
We are given the total simple interest earned over 4 years at an annual interest rate of 8%.
Our objective is to determine the original sum of money invested, which is the Principal ($P$).

Step 2: Key Formula or Approach:
The formula for calculating Simple Interest ($SI$) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
$\bullet$ $SI$ is the simple interest earned,
$\bullet$ $P$ is the principal amount,
$\bullet$ $R$ is the annual rate of interest,
$\bullet$ $T$ is the time period in years.

Step 3: Detailed Explanation:
$\bullet$ Let us identify the values given in the problem statement.
$\bullet$ Simple Interest ($SI$) = Rs 1,920.
$\bullet$ Rate of Interest ($R$) = 8% per annum.
$\bullet$ Time period ($T$) = 4 years.
$\bullet$ We need to find the Principal ($P$).
$\bullet$ Substituting the known values into the Simple Interest formula:
\[ 1920 = \frac{P \times 8 \times 4}{100} \]
$\bullet$ Simplifying the right side of the equation:
\[ 1920 = \frac{32P}{100} \]
$\bullet$ Now, rearrange the equation to solve for $P$:
\[ 32P = 1920 \times 100 \]
\[ P = \frac{1920 \times 100}{32} \]
$\bullet$ Simplifying the fraction:
Since $192 \div 32 = 6$, we have $1920 \div 32 = 60$.
\[ P = 60 \times 100 \]
\[ P = 6000 \]
$\bullet$ Thus, the principal amount is Rs 6,000.

Step 4: Final Answer:
The principal sum of money is Rs 6,000.
Therefore, the correct option is (B).