Question

How much time will it take for an amount of 450 to yield 81 as interest at $4.5%$ per annum of simple interest?

• A. 3 years
• B. 2 years
• C. 4 years
• D. 5 years

Hint:

To simplify the decimal calculation, write \(4.5%\) as \(\frac{9}{2}%\).
\[ 81 = \frac{450 \times \frac{9}{2} \times T}{100} \]
\[ 81 = \frac{225 \times 9 \times T}{100} \]
Divide both sides by 9:
\[ 9 = \frac{225 \times T}{100} \implies 9 = 2.25 \times T \]
Since \(2.25 \times 4 = 9\), we get \(T = 4\) years. This avoids tedious decimal multiplications.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the time duration required for a specific principal sum to accumulate a given simple interest amount at a specified annual simple interest rate.
We are given the principal, the interest earned, and the rate, and we need to solve for time.

Step 2: Key Formula or Approach:
The basic formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Rearranging the formula to solve for Time (\(T\)):
\[ T = \frac{SI \times 100}{P \times R} \]
Where:
\(P\) is the Principal amount = 450.
\(SI\) is the Simple Interest = 81.
\(R\) is the annual Rate of Interest = \(4.5%\).

Step 3: Detailed Explanation:
$\bullet$ Substituting the Given Values:
We substitute the given values into our rearranged equation:
\[ T = \frac{81 \times 100}{450 \times 4.5} \]
$\bullet$ Simplifying the Expression:
Let's first simplify the denominator:
\[ 450 \times 4.5 = 45 \times 45 = 2025 \]
Now, substitute this value back into the numerator:
\[ T = \frac{8100}{2025} \]
$\bullet$ Step-by-step Division:
Dividing both the numerator and the denominator by 9:
\[ T = \frac{900}{225} \]
Dividing further by 25:
\[ T = \frac{36}{9} \]
\[ T = 4 \text{ years} \]

Step 4: Final Answer:
The time required to yield an interest of 81 is 4 years.