Ahmed has a recurring deposit account in a bank. He deposits Rs 2,500 per month for 2 years. If the gets Rs 66,250 at the time of maturity, find :
The rate of interest.

Answer

To find the rate of interest for Ahmed's recurring deposit account, we can follow these steps:

### Step 1: Calculate the total amount deposited
Ahmed deposits Rs 2,500 per month for 2 years.

\[ \text{Total months} = 2 \times 12 = 24 \text{ months} \]

\[ \text{Total amount deposited} = \text{Monthly deposit} \times \text{Total months} = 2500 \times 24 = 60000 \text{ Rs} \]

### Step 2: Calculate the interest earned
The total amount received at maturity is Rs 66,250.

\[ \text{Interest} = \text{Total amount at maturity} - \text{Total amount deposited} = 66250 - 60000 = 6250 \text{ Rs} \]

### Step 3: Calculate the time period in years for the interest calculation
In a recurring deposit account, the time period (T) is calculated using the formula:

\[ T = \frac{n(n+1)}{24} \]

Where \( n \) is the number of months. Here, \( n = 24 \).

\[ T = \frac{24(24 + 1)}{24} = 25 \text{ months} \]

To convert this into years:

\[ T = \frac{25}{12} \text{ years} \]

### Step 4: Use the simple interest formula to find the rate of interest
The formula for simple interest is:

\[ \text{Interest} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal (Total amount deposited) = Rs 60,000
- \( R \) = Rate of interest (unknown)
- \( T \) = Time in years = \( \frac{25}{12} \)

Substituting the values into the formula:

\[ 6250 = \frac{60000 \times R \times \frac{25}{12}}{100} \]

### Step 5: Solve for R
Rearranging the equation to find \( R \):

\[ 6250 = \frac{60000 \times R \times 25}{1200} \]

Multiplying both sides by 1200:

\[ 6250 \times 1200 = 60000 \times R \times 25 \]

Calculating \( 6250 \times 1200 \):

\[ 7500000 = 60000 \times R \times 25 \]

Now, simplifying:

\[ 7500000 = 1500000R \]

Dividing both sides by 1500000:

\[ R = \frac{7500000}{1500000} = 5 \]

### Final Result
The rate of interest \( R \) is:

\[ R = 5\% \]