Find the present worth of Rs 9000 due for 4 years hence the rate of interest being 5% p.a.

Options

A. Rs 8000
B. Rs 7800
C. Rs 7500
D. Rs 8100

Answer

To find the present worth of Rs 9000 due in 4 years at an interest rate of 5% per annum, we can use the formula for present worth (PV):

\[ PV = \frac{A}{(1 + r)^t} \]

Where:
- \(PV\) = Present Worth
- \(A\) = Amount due in the future (Rs 9000)
- \(r\) = Rate of interest per annum (5% = 0.05)
- \(t\) = Time in years (4 years)

### Step-by-Step Solution:

1. **Identify the values:**
- Amount (A) = Rs 9000
- Rate (r) = 5% = 0.05
- Time (t) = 4 years

2. **Substitute the values into the formula:**
\[ PV = \frac{9000}{(1 + 0.05)^4} \]

3. **Calculate \( (1 + r)^t \):**
\[ (1 + 0.05)^4 = (1.05)^4 \]
Now calculate \( (1.05)^4 \):
\[ (1.05)^4 = 1.21550625 \quad \text{(approximately)} \]

4. **Substitute this back into the formula:**
\[ PV = \frac{9000}{1.21550625} \]

5. **Calculate the present worth:**
\[ PV \approx \frac{9000}{1.21550625} \approx 7407.79 \]

6. **Round to the nearest whole number:**
\[ PV \approx 7408 \quad \text{(but we need to check the options)} \]

7. **Check the options provided:**
The closest option to Rs 7408 is Rs 7500.

### Final Answer:
The present worth of Rs 9000 due in 4 years at an interest rate of 5% per annum is approximately Rs 7500.

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