Lussy deposited Rs 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which she will receive after 9 months?

Options

A. 8000
B. 8195.45
C. 8456.23
D. 8756.24

Answer

To solve the problem of how much Lussy will receive after 9 months with a principal of Rs 7500 and an interest rate of 12% per annum compounded quarterly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 7500
- Rate of interest (R) = 12% per annum
- Time (T) = 9 months = 9/12 years = 0.75 years
- Compounding frequency (n) = 4 (since interest is compounded quarterly)

### Step 2: Convert the annual interest rate to a quarterly rate
The quarterly interest rate (r) can be calculated as:
\[ r = \frac{R}{n} = \frac{12\%}{4} = 3\% \]
In decimal form, this is:
\[ r = \frac{3}{100} = 0.03 \]

### Step 3: Calculate the number of compounding periods
The total number of compounding periods (nT) for 9 months is:
\[ nT = n \times T = 4 \times 0.75 = 3 \]

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + r\right)^{nT} \]
Substituting the known values:
\[ A = 7500 \left(1 + 0.03\right)^{3} \]

### Step 5: Calculate the amount
First, calculate \( (1 + 0.03)^{3} \):
\[ (1 + 0.03)^{3} = (1.03)^{3} \]
Calculating \( (1.03)^{3} \):
\[ (1.03)^{3} = 1.092727 \] (approximately)

Now substitute this back into the formula:
\[ A = 7500 \times 1.092727 \]
\[ A \approx 8195.45 \]

### Step 6: Final amount
Thus, the amount Lussy will receive after 9 months is approximately Rs 8195.45.