Mr. Richard has a recurring deposite account in a bank for 3 years at 7.5% p.a. simple interest. If he gets Rs 8325 as interest at the time of maturity, find the maturity value.

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Understand the Problem
Mr. Richard has a recurring deposit account for 3 years at a simple interest rate of 7.5% per annum. He receives Rs. 8325 as interest at maturity, and we need to find the maturity value.

### Step 2: Identify the Variables
- Interest (I) = Rs. 8325
- Rate of interest (R) = 7.5% per annum
- Time (T) = 3 years
- Total number of months (N) = 3 years × 12 months/year = 36 months

### Step 3: Use the Formula for Simple Interest
The formula for simple interest is:
\[ I = P \times R \times T \]
Where:
- \( P \) is the principal amount (total deposits)
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

### Step 4: Calculate the Monthly Installment (P)
For a recurring deposit, the total principal deposited can be calculated using the formula:
\[ P = \frac{I \times 100 \times 12}{(N + 1) \times N \times R} \]
Substituting the known values:
- \( I = 8325 \)
- \( N = 36 \)
- \( R = 7.5 \)

Now substituting these values into the formula:
\[ P = \frac{8325 \times 100 \times 12}{(36 + 1) \times 36 \times 7.5} \]

### Step 5: Simplify the Calculation
Calculating the denominator:
- \( N + 1 = 37 \)
- \( N = 36 \)
- \( R = 7.5 \)

Now calculating:
\[ P = \frac{8325 \times 100 \times 12}{37 \times 36 \times 7.5} \]

Calculating the denominator:
\[ 37 \times 36 = 1332 \]
\[ 1332 \times 7.5 = 9990 \]

Now substituting back:
\[ P = \frac{8325 \times 1200}{9990} \]

Calculating the numerator:
\[ 8325 \times 1200 = 9990000 \]

Now dividing:
\[ P = \frac{9990000}{9990} = 1000 \]

### Step 6: Calculate the Maturity Value
The maturity value (MV) is given by:
\[ MV = (N \times P) + I \]
Where:
- \( N = 36 \)
- \( P = 2000 \)
- \( I = 8325 \)

Substituting the values:
\[ MV = (36 \times 2000) + 8325 \]
\[ MV = 72000 + 8325 = 80325 \]

### Final Answer
The maturity value is Rs. 80325.

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