Mr Akhil invested Rs 13,500 in FD. How much will he get on maturity if the invested it at 20% per annum compound interest for 6 months compounded quarterly?

Options

A. Rs. 14,883.35
B. Rs. 14,883.75
C. Rs. 14,883.5
D. Rs. 14,883

Answer

To determine how much Mr. Akhil will receive on maturity after investing Rs 13,500 at 20% per annum compound interest for 6 months compounded quarterly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 13,500
- Annual Interest Rate (R) = 20%
- Time (T) = 6 months

### Step 2: Adjust the interest rate for quarterly compounding
Since the interest is compounded quarterly, we need to divide the annual interest rate by 4:
- Quarterly Interest Rate = R / 4 = 20% / 4 = 5%

### Step 3: Convert the time period into quarters
The time period of 6 months is equivalent to:
- Time in quarters = 6 months / 3 months per quarter = 2 quarters

### Step 4: Use the compound interest formula
The formula for the amount (A) after compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- P = Principal amount
- R = Quarterly interest rate
- T = Number of quarters

Substituting the values:
\[ A = 13500 \left(1 + \frac{5}{100}\right)^2 \]

### Step 5: Calculate the amount
First, calculate \(1 + \frac{5}{100}\):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]

Now, raise this to the power of 2 (since T = 2):
\[ (1.05)^2 = 1.1025 \]

Now, substitute this back into the formula:
\[ A = 13500 \times 1.1025 \]

Calculating this gives:
\[ A = 13500 \times 1.1025 = 14888.75 \]

### Step 6: Final amount
Thus, the amount Mr. Akhil will receive on maturity is Rs 14,888.75.

### Summary
Mr. Akhil will receive Rs 14,888.75 on maturity after investing Rs 13,500 at 20% per annum compound interest for 6 months compounded quarterly.

---