Question

In 4 years, the simple interest (SI) on a certain sum of money is \(\frac{7}{25}\) of the principal. What is the annual rate of interest?

• A. 4%
• B. 4.5%
• C. 7%
• D. 9%

Hint:

Use \(SI = \frac{PTR}{100}\) with \(SI = \frac{7}{25}P\) and \(T = 4\); cancel \(P\) and solve for \(R\).

Answer 1

The Correct Option is C

Step 1: Write down the simple interest formula.
Simple interest is given by \( SI = \dfrac{P \times T \times R}{100} \), where \(P\) is the principal, \(T\) is the time in years, and \(R\) is the annual rate of interest in percent.

Step 2: Note what the question gives.
The time is \(T = 4\) years.
The interest earned equals \( \dfrac{7}{25} \) of the principal, so \( SI = \dfrac{7}{25}P \).

Step 3: Substitute into the formula.
\[ \frac{7}{25}P = \frac{P \times 4 \times R}{100} \]
P appears on both sides and is never zero, so cancel it.
\[ \frac{7}{25} = \frac{4R}{100} \]

Step 4: Solve for R.
Cross multiply: \( 7 \times 100 = 25 \times 4 \times R \).
\[ 700 = 100R \]
\[ R = 7 \]

Step 5: Check this against the other options.
A rate of 4% would give \( SI = \frac{4 \times 4}{100}P = \frac{16}{100}P \), which is smaller than \(\frac{7}{25}P = \frac{28}{100}P\).
A rate of 4.5% gives \(\frac{18}{100}P\), still short of \(\frac{28}{100}P\).
A rate of 9% gives \(\frac{36}{100}P\), which overshoots it. Only 7% lands exactly on \(\frac{28}{100}P\).

Final Answer:
The annual rate of interest is 7%.
\[ \boxed{R = 7\%} \]