Question

The simple interest on a sum of money is equal to the principal and number of years is equal to the rate percent per annum. Find the rate percent.

• A. 15%
• B. 20%
• C. 12%
• D. 10%

Answer 1

Answer:

D. 10%

The rate percent is 10% per annum.

1. Understand the Given Information

• Let the Principal be $P$.

• Simple Interest ($SI$) is equal to the principal: $SI = P$

• Number of years ($T$) is equal to the rate percent ($R$): $T = R$

2. Apply the Simple Interest Formula

The formula for Simple Interest is:
$SI = \frac{P \times R \times T}{100}$

3. Substitute the Values

Replace $SI$ with $P$ and $T$ with $R$:
$P = \frac{P \times R \times R}{100}$

4. Solve for R

Divide both sides by $P$:
$1 = \frac{R^2}{100}$

Multiply both sides by 100:
$R^2 = 100$

Take the square root of both sides:
$R = \sqrt{100} = \mathbf{10}$