Mahima has a recurring deposite account in a book for 3 years at 8 % P.a. if she gets rupes 3,996 as interest at the time of maturity of the scheme ,find :
the monthly instalment
(ii) the maturity amount.

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Interest (I) = Rs. 3996
- Time (n) = 3 years = 36 months (since 1 year = 12 months)
- Rate of interest (r) = 8% per annum

### Step 2: Use the formula for interest on a recurring deposit
The formula for the interest earned on a recurring deposit is:
\[ I = \frac{P \cdot n \cdot (n + 1)}{2 \cdot 12 \cdot 100} \cdot r \]
Where:
- \( P \) = monthly installment
- \( n \) = total number of months
- \( r \) = rate of interest per annum

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 3996 = \frac{P \cdot 36 \cdot (36 + 1)}{2 \cdot 12 \cdot 100} \cdot 8 \]

### Step 4: Simplify the equation
Calculating \( (36 + 1) = 37 \):
\[ 3996 = \frac{P \cdot 36 \cdot 37}{2 \cdot 12 \cdot 100} \cdot 8 \]
Now, simplifying the denominator:
\[ 2 \cdot 12 = 24 \quad \text{and} \quad 24 \cdot 100 = 2400 \]
So, we can rewrite the equation as:
\[ 3996 = \frac{P \cdot 36 \cdot 37 \cdot 8}{2400} \]

### Step 5: Rearranging to find \( P \)
Multiplying both sides by 2400:
\[ 3996 \cdot 2400 = P \cdot 36 \cdot 37 \cdot 8 \]
Calculating \( 3996 \cdot 2400 \):
\[ P \cdot 36 \cdot 37 \cdot 8 = 9590400 \]
Now, dividing both sides by \( 36 \cdot 37 \cdot 8 \):
\[ P = \frac{9590400}{36 \cdot 37 \cdot 8} \]

### Step 6: Calculate \( 36 \cdot 37 \cdot 8 \)
Calculating \( 36 \cdot 37 = 1332 \):
\[ 1332 \cdot 8 = 10656 \]
So, we have:
\[ P = \frac{9590400}{10656} \]

### Step 7: Final calculation for \( P \)
Calculating \( P \):
\[ P = 900 \]

### Step 8: Calculate the maturity amount
The maturity amount (M) can be calculated using the formula:
\[ M = P \cdot n + I \]
Substituting the values:
\[ M = 900 \cdot 36 + 3996 \]
Calculating \( 900 \cdot 36 = 32400 \):
\[ M = 32400 + 3996 = 36396 \]

### Final Answers
1. Monthly Installment (P) = Rs. 900
2. Maturity Amount (M) = Rs. 36396