Math Snap

STEP 1

1. The principal amount is P16,000.
2. The interest earned is P480.
3. The time period is 9 months.
4. We need to find the annual rate of interest.
5. The interest is simple interest.

STEP 2

1. Understand the formula for simple interest.
2. Convert the time period to years.
3. Substitute the known values into the simple interest formula.
4. Solve for the annual rate of interest.

STEP 3

Understand the formula for simple interest. The formula is:
$$\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}$$ Where:
- $P$ is the principal amount.
- $R$ is the rate of interest per annum.
- $T$ is the time period in years.

STEP 4

Convert the time period to years. Since the time given is 9 months, convert it to years:
$$T = \frac{9}{12} = \frac{3}{4} \text{ years}$$

STEP 5

Substitute the known values into the simple interest formula. We know:
- $\text{SI} = 480$
- $P = 16,000$
- $T = \frac{3}{4}$
Substitute these into the formula:
$$480 = \frac{16,000 \times R \times \frac{3}{4}}{100}$$

Solve for the annual rate of interest $R$.
First, simplify the equation:
$$480 = \frac{16,000 \times R \times 0.75}{100}$$ $$480 = \frac{12,000R}{100}$$ $$480 = 120R$$ Now, solve for $R$:
$$R = \frac{480}{120}$$ $$R = 4$$ The annual rate of interest is:
$\boxed{4\%}$