Find the compound interest on X 31250 at 16% pa compounded quarterly for 9 months.

Options

A. X 4000
B. X 3902
C. X 3500
D. X4200

Answer

To find the compound interest on ₹31,250 at an interest rate of 16% per annum compounded quarterly for 9 months, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹31,250
- Annual Interest Rate (R) = 16%
- Time (T) = 9 months

### Step 2: Convert the annual interest rate to a quarterly interest rate
Since the interest is compounded quarterly, we need to divide the annual interest rate by 4:
\[ \text{Quarterly Rate} = \frac{R}{4} = \frac{16\%}{4} = 4\% \]

### Step 3: Convert the time period from months to quarters
Since the interest is compounded quarterly, we need to convert the time period from months to quarters:
\[ \text{Time in years} = \frac{9 \text{ months}}{12} = \frac{3}{4} \text{ years} \]
To convert this to quarters:
\[ \text{Time in quarters} = \frac{9 \text{ months}}{3 \text{ months/quarter}} = 3 \text{ quarters} \]

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal
- \( r \) = Rate of interest per period
- \( n \) = Number of periods

Substituting the values:
\[ A = 31250 \left(1 + \frac{4}{100}\right)^3 \]
\[ A = 31250 \left(1 + 0.04\right)^3 \]
\[ A = 31250 \left(1.04\right)^3 \]

### Step 5: Calculate \( (1.04)^3 \)
Calculating \( (1.04)^3 \):
\[ (1.04)^3 = 1.124864 \]

### Step 6: Calculate the total amount \( A \)
Now substitute back to find \( A \):
\[ A = 31250 \times 1.124864 \approx 35152.00 \]

### Step 7: Calculate the compound interest
The compound interest (CI) can be calculated as:
\[ CI = A - P \]
Substituting the values:
\[ CI = 35152.00 - 31250 = 3902.00 \]

### Final Answer
The compound interest on ₹31,250 at 16% per annum compounded quarterly for 9 months is approximately ₹3,902.00.

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