Mrs. Karna has a recurring deposit account in Punjab National Bank for 3 years at 8% p.a. If she gets Rs 9,990 as interest at the time of maturity, Find:
(a) the monthly installment (b) the maturity level

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- Time period (n) = 3 years
- Interest (I) = Rs 9,990
- Rate of interest (r) = 8% per annum

### Step 2: Convert the time period into months
Since the recurring deposit is made monthly, we need to convert the time period into months:
\[ n = 3 \text{ years} = 3 \times 12 = 36 \text{ months} \]

### Step 3: Set up the formula for interest earned in a recurring deposit
The formula for the interest earned (I) in a recurring deposit account is given by:
\[ I = \frac{P \times n \times (n + 1)}{2400} \]
Where:
- \( P \) = monthly installment
- \( n \) = number of months

### Step 4: Substitute the known values into the formula
We know:
- \( I = 9,990 \)
- \( n = 36 \)

Substituting these values into the formula:
\[ 9,990 = \frac{P \times 36 \times (36 + 1)}{2400} \]
\[ 9,990 = \frac{P \times 36 \times 37}{2400} \]

### Step 5: Simplify the equation
Calculating \( 36 \times 37 \):
\[ 36 \times 37 = 1332 \]
So the equation becomes:
\[ 9,990 = \frac{P \times 1332}{2400} \]

### Step 6: Cross-multiply to solve for \( P \)
Cross-multiplying gives:
\[ 9,990 \times 2400 = P \times 1332 \]
Calculating \( 9,990 \times 2400 \):
\[ 9,990 \times 2400 = 23,976,000 \]
Thus, we have:
\[ 23,976,000 = P \times 1332 \]

### Step 7: Solve for \( P \)
Now, divide both sides by 1332:
\[ P = \frac{23,976,000}{1332} \]
Calculating this gives:
\[ P \approx 18,000 \]

### Step 8: Calculate the maturity level
The maturity value (M) can be calculated using the formula:
\[ M = P \times n + I \]
Substituting the values:
\[ M = 18,000 \times 36 + 9,990 \]
Calculating \( 18,000 \times 36 \):
\[ 18,000 \times 36 = 648,000 \]
Now adding the interest:
\[ M = 648,000 + 9,990 = 657,990 \]

### Final Answers
(a) Monthly Installment \( P \) = Rs 18,000
(b) Maturity Level \( M \) = Rs 657,990