What amount will be received on a sum of 15000 in 5/4 year at 12% pa, if interest is compounded quarterly ?

Options

A. 16596.88
B. 16789.08
C. 17630.77
D. 17389.12

Answer

To solve the problem of finding the amount received on a sum of 15,000 in 5/4 years at 12% per annum, compounded quarterly, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = 15,000
- Rate of interest (R) = 12% per annum
- Time (T) = 5/4 years
- Compounding frequency = Quarterly

### Step 2: Convert the time into quarters
Since the interest is compounded quarterly, we need to convert the time from years into quarters:
- Number of quarters in 5/4 years = (5/4) * 4 = 5 quarters

### Step 3: Adjust the rate of interest for quarterly compounding
Since the interest is compounded quarterly, we need to divide the annual interest rate by 4:
- Quarterly interest rate = R/4 = 12% / 4 = 3%

### 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 \( T \)
- \( P \) = Principal amount
- \( r \) = Rate of interest per period
- \( n \) = Number of compounding periods

Substituting the values:
- \( A = 15000 \left(1 + \frac{3}{100}\right)^5 \)

### Step 5: Calculate the amount
First, calculate \( 1 + \frac{3}{100} \):
\[ 1 + \frac{3}{100} = 1.03 \]

Now, raise this to the power of 5:
\[ 1.03^5 \]

Calculating \( 1.03^5 \):
\[ 1.03^5 \approx 1.159274 \]

Now, substitute this back into the amount formula:
\[ A = 15000 \times 1.159274 \]

Calculating the final amount:
\[ A \approx 17389.11 \]

### Final Answer
The amount received after 5/4 years is approximately **17,389.11**.

---