A certain amount is invested in a scheme of simple interest. It amounts to Rs 3600 in 5 years and Rs 4560 in 8 years. What is the rate of interest (in percentage)?

Options

A. 14
B. 24
C. 16
D. 20

Answer

To find the rate of interest for the given problem, we can follow these steps:

### Step 1: Determine the Interest Earned Between the Two Time Periods
We know the amount after 5 years is Rs 3600 and after 8 years is Rs 4560. The interest earned between these two periods (3 years) can be calculated as follows:

\[ \text{Interest for 3 years} = \text{Amount after 8 years} - \text{Amount after 5 years} = 4560 - 3600 = 960 \text{ Rs} \]

### Step 2: Calculate the Annual Interest
Since the interest of Rs 960 is earned over 3 years, we can find the interest earned per year:

\[ \text{Annual Interest} = \frac{\text{Interest for 3 years}}{3} = \frac{960}{3} = 320 \text{ Rs} \]

### Step 3: Calculate the Total Interest for 5 Years
Now, we can calculate the total interest earned over 5 years:

\[ \text{Total Interest for 5 years} = \text{Annual Interest} \times 5 = 320 \times 5 = 1600 \text{ Rs} \]

### Step 4: Determine the Principal Amount
The total amount after 5 years is Rs 3600, which is the sum of the principal amount and the interest earned over 5 years. We can find the principal amount (Cost):

\[ \text{Principal} = \text{Amount after 5 years} - \text{Total Interest for 5 years} = 3600 - 1600 = 2000 \text{ Rs} \]

### Step 5: Use the Simple Interest Formula to Find the Rate
The formula for simple interest is:

\[ \text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]

We know the simple interest for 1 year is Rs 320, the principal is Rs 2000, and we need to find the rate. Rearranging the formula gives us:

\[ \text{Rate} = \frac{\text{Simple Interest} \times 100}{\text{Principal} \times \text{Time}} \]

Substituting the values we have:

\[ \text{Rate} = \frac{320 \times 100}{2000 \times 1} = \frac{32000}{2000} = 16\% \]

### Final Answer
The rate of interest is **16%**.

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