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: Pick a convenient principal.
The interest is a fraction with denominator 25, so let the principal be $P = 25$. Any multiple of 25 works, since the rate does not depend on the actual size of $P$.

Step 2: Find the total interest earned.
Interest over 4 years $= \frac{7}{25} \times 25 = 7$.

Step 3: Find the interest earned per year.
Interest per year $= \frac{7}{4} = 1.75$.

Step 4: Convert this yearly interest into a rate percent.
Rate percent $= \frac{\text{interest per year}}{\text{principal}} \times 100 = \frac{1.75}{25} \times 100$.
\[ \frac{1.75}{25} \times 100 = \frac{175}{25} = 7 \]

Step 5: Match with the options.
A rate of 7% is exactly option C. None of the other rates (4%, 4.5%, 9%) reproduce an interest of 7 on a principal of 25 over 4 years.

Final Answer:
The annual rate of interest works out to 7%. \[ \boxed{7\%} \]