The maturity value of a recurring deposit account is Rs 42,400. If the account is held for 2 years and the rate of interest is 10% per annum, find the amount of each monthly instalment.

Answer

To find the amount of each monthly installment for a recurring deposit account, we can follow these steps:

### Step 1: Understand the given information
- Maturity value (M) = Rs 42,400
- Time period (n) = 2 years = 24 months
- Rate of interest (r) = 10% per annum

### Step 2: Let the monthly installment be Rs V
We denote the monthly installment as V.

### Step 3: Calculate the total principal amount
The total principal amount (P) deposited over 24 months is:
\[ P = V \times n = V \times 24 \]

### Step 4: Calculate the interest earned
The interest earned on the recurring deposit can be calculated using the formula for the interest on a recurring deposit:
\[ \text{Interest} = \frac{P \times r \times t}{100} \]
Where:
- P = Total principal
- r = Rate of interest
- t = Time in years

Since the interest is calculated for each installment separately, we need to consider that the first installment earns interest for 24 months, the second for 23 months, and so on, until the last installment which earns interest for 1 month.

The total interest can also be calculated using the formula:
\[ \text{Total Interest} = \frac{V \times n \times (n + 1)}{2} \times \frac{r}{100 \times 12} \]
Substituting the values we have:
\[ \text{Total Interest} = \frac{V \times 24 \times 25}{2} \times \frac{10}{100 \times 12} \]
\[ \text{Total Interest} = \frac{V \times 600}{2} \times \frac{10}{1200} \]
\[ \text{Total Interest} = V \times 300 \times \frac{1}{120} \]
\[ \text{Total Interest} = \frac{V \times 300}{120} = \frac{5V}{2} \]

### Step 5: Set up the equation for maturity value
The maturity value (M) is the sum of the total principal and the total interest:
\[ M = P + \text{Total Interest} \]
Substituting the values:
\[ 42400 = V \times 24 + \frac{5V}{2} \]

### Step 6: Solve the equation
To solve for V, we first express everything in terms of V:
\[ 42400 = 24V + \frac{5V}{2} \]
To eliminate the fraction, we can multiply the entire equation by 2:
\[ 84800 = 48V + 5V \]
Combine like terms:
\[ 84800 = 53V \]

Now, divide both sides by 53:
\[ V = \frac{84800}{53} \]
Calculating this gives:
\[ V = 1600 \]

### Final Answer
The amount of each monthly installment is Rs 1600.

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