Mr. Sriram invested Rs.14,000 in FD. How much will he get on maturity, if he invested it at 20% per annum compound interest for 6 months, compounded quarterly?

Options

A. Rs. 15,437
B. Rs. 15,434
C. Rs. 15,436
D. Rs. 15,435

Answer

To solve the problem step by step, we will calculate the maturity amount Mr. Sriram will receive after investing Rs. 14,000 at a compound interest rate of 20% per annum for 6 months, compounded quarterly.

### Step 1: Identify the given values
- Principal (P) = Rs. 14,000
- Annual Interest Rate (R) = 20% per annum
- Time (T) = 6 months = 0.5 years
- Compounding Frequency (n) = Quarterly = 4 times a year

### Step 2: Calculate the quarterly interest rate
The quarterly interest rate can be calculated as follows:
\[ \text{Quarterly Interest Rate} = \frac{R}{n} = \frac{20\%}{4} = 5\% \]

### Step 3: Determine the number of compounding periods
Since the interest is compounded quarterly and the total time is 6 months, the number of compounding periods (t) will be:
\[ t = n \times \text{Time in years} = 4 \times 0.5 = 2 \text{ quarters} \]

### Step 4: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \(A\) = Amount on maturity
- \(P\) = Principal
- \(r\) = Quarterly interest rate
- \(n\) = Number of compounding periods

Substituting the values:
\[ A = 14000 \left(1 + \frac{5}{100}\right)^2 \]

### Step 5: Calculate the amount
First, calculate \(1 + \frac{5}{100}\):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]
Now raise it to the power of 2:
\[ (1.05)^2 = 1.1025 \]
Now calculate \(A\):
\[ A = 14000 \times 1.1025 = 15435 \]

### Conclusion
The maturity amount Mr. Sriram will receive is Rs. 15,435.