Calculating Simple Interest Rate Per Annum

This problem involves calculating the simple rate of interest per annum given the principal amount, the time period, and the simple interest earned. Simple interest is calculated only on the initial principal amount.

Understanding Simple Interest Calculation

The formula for simple interest is:

$\text{SI} = \frac{P \times R \times T}{100}$

Where:

• $\text{SI}$ is the Simple Interest
• $P$ is the Principal amount
• $R$ is the Rate of Interest per annum
• $T$ is the Time period in years

Applying the Formula to Find the Rate

We are given:

• Principal ($P$) = Rs. 750
• Time ($T$) = 3 months
• Simple Interest ($\text{SI}$) = Rs. 18

We need to find the Rate of Interest ($R$) per annum.

First, we must convert the time from months to years. Since there are 12 months in a year, 3 months is equal to $\frac{3}{12}$ years.

$T = \frac{3}{12} \text{ years} = \frac{1}{4} \text{ years} = 0.25 \text{ years}$

Now, we can rearrange the simple interest formula to solve for $R$:

$R = \frac{\text{SI} \times 100}{P \times T}$

Substitute the given values into the formula:

$R = \frac{18 \times 100}{750 \times 0.25}$

$R = \frac{1800}{187.5}$

Now, perform the calculation:

$R = 9.6$

So, the simple rate of interest per annum is 9.6%.

Step-by-Step Simple Interest Rate Calculation

1. Identify the given values: Principal ($P=750$), Time ($T=3$ months), Simple Interest ($\text{SI}=18$).
2. Convert Time to years: $T = 3 \text{ months} = \frac{3}{12} \text{ years} = 0.25 \text{ years}$.
3. Use the rearranged formula for the rate: $R = \frac{\text{SI} \times 100}{P \times T}$.
4. Substitute the values: $R = \frac{18 \times 100}{750 \times 0.25}$.
5. Calculate the numerator: $18 \times 100 = 1800$.
6. Calculate the denominator: $750 \times 0.25 = 187.5$.
7. Divide the numerator by the denominator: $R = \frac{1800}{187.5} = 9.6$.
8. State the result: The rate is 9.6% per annum.

The calculated simple rate of interest per annum is 9.6%.

Revision Table: Simple Interest Key Concepts

Additional Information on Interest Calculations

Understanding how interest is calculated is fundamental in finance. Simple interest is a basic form, but there are other types like compound interest.

• Compound Interest: Unlike simple interest, compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. The formula is $A = P(1 + \frac{R}{100})^T$, where A is the amount after T years. Compound interest leads to faster growth of investment or debt over time compared to simple interest.
• Time Units: It is crucial to ensure that the time period ($T$) and the rate of interest ($R$) are in compatible units. If the rate is per annum, the time must be in years. If the time is given in months or days, it must be converted to years accordingly ($T \text{ in years} = \frac{\text{Number of months}}{12}$ or $T \text{ in years} = \frac{\text{Number of days}}{365}$).

This problem specifically focused on simple interest and required careful conversion of the time unit to match the per annum rate requirement.