If you invest 100 rupee at 40% annual interest compounded quarterly, how much will you receive after one year?

Options

A. 145.61
B. 146.41
C. 149.01
D. 148.11

Answer

To solve the problem of how much you will receive after investing 100 rupees at a 40% annual interest rate compounded quarterly for one year, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = 100 rupees
- Annual interest rate (R) = 40% = 0.40 (as a decimal)
- Time (T) = 1 year
- Compounding frequency (n) = 4 (since it is compounded quarterly)

### Step 2: Calculate the quarterly interest rate
Since the interest is compounded quarterly, we need to divide the annual interest rate by the number of compounding periods in a year:
\[ \text{Quarterly interest rate} = \frac{R}{n} = \frac{0.40}{4} = 0.10 \text{ or } 10\% \]

### Step 3: Calculate the total number of compounding periods
Since the interest is compounded quarterly and the time is 1 year, the total number of compounding periods (nT) will be:
\[ nT = n \times T = 4 \times 1 = 4 \]

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \]
Substituting the values we have:
\[ A = 100 \left(1 + 0.10\right)^{4} \]
\[ A = 100 \left(1.10\right)^{4} \]

### Step 5: Calculate \( (1.10)^{4} \)
Now we need to calculate \( (1.10)^{4} \):
\[ (1.10)^{4} = 1.4641 \]

### Step 6: Calculate the final amount
Now substitute back to find A:
\[ A = 100 \times 1.4641 = 146.41 \]

### Conclusion
After one year, the amount you will receive is **146.41 rupees**.

---