What is the compound interest earned on Rs 80,000 at 40% per annum in 1 year compounded quarterly?

Options

A. 28317
B. 37128
C. 18732
D. 21387

Answer

To calculate the compound interest earned on Rs 80,000 at an interest rate of 40% per annum compounded quarterly for 1 year, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 80,000
- Rate of interest (R) = 40% per annum
- Time (T) = 1 year
- Number of times interest is compounded per year (n) = 4 (quarterly)

### Step 2: Convert the annual interest rate to a quarterly interest rate
The quarterly interest rate (r) can be calculated as follows:
\[ r = \frac{R}{n} = \frac{40\%}{4} = 10\% = \frac{10}{100} = 0.10 \]

### Step 3: Calculate the total amount (A) after 1 year using the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Substituting the values we have:
\[ A = 80,000 \left(1 + 0.10\right)^{4 \times 1} \]
\[ A = 80,000 \left(1.10\right)^{4} \]

### Step 4: Calculate \( (1.10)^{4} \)
Now we need to calculate \( (1.10)^{4} \):
\[ (1.10)^{4} = 1.4641 \]

### Step 5: Calculate the total amount (A)
Now substitute back to find A:
\[ A = 80,000 \times 1.4641 \]
\[ A = 117,128 \]

### Step 6: Calculate the compound interest (CI)
The compound interest can be calculated using the formula:
\[ CI = A - P \]
Substituting the values:
\[ CI = 117,128 - 80,000 \]
\[ CI = 37,128 \]

### Final Answer
The compound interest earned on Rs 80,000 at 40% per annum compounded quarterly for 1 year is Rs 37,128.

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