A property dealer bought a rectangular plot (of land) in Noida 5 years ago at the rate of Rs. 1000 per `m^2` . The cost of plot is increases by 5% in every 6 years and the worth of a rupee falls down at a rate of 2% in every 5 years . What is the approximate value of the land per meter 25 years hence ??

Options

A. Rs. 995
B. Rs. 1134
C. Rs. 1500
D. Rs. 1495

Answer

To solve the problem step by step, we need to determine the future value of the land per square meter after 25 years from now, considering both the appreciation in land value and the depreciation of currency value.

### Step 1: Determine the initial cost of the land
The initial cost of the land was Rs. 1000 per m².

### Step 2: Calculate the number of periods for land value appreciation
The land appreciates at a rate of 5% every 6 years. Since we are looking for the value 25 years from now, we need to consider the total time from the purchase date, which is 30 years (5 years ago + 25 years hence).

To find out how many 6-year periods fit into 30 years:
\[ \text{Number of periods} = \frac{30}{6} = 5 \]

### Step 3: Calculate the appreciation factor for the land
The appreciation factor for each 6-year period is given by:
\[ \text{Appreciation factor} = 1 + \frac{5}{100} = 1.05 \]
Thus, the total appreciation factor over 5 periods is:
\[ \text{Total appreciation factor} = (1.05)^5 \]

### Step 4: Calculate the total appreciation
Calculating \( (1.05)^5 \):
\[ (1.05)^5 \approx 1.27628 \]
Now, we can find the appreciated value of the land:
\[ \text{Appreciated value} = 1000 \times 1.27628 \approx 1276.28 \text{ Rs/m²} \]

### Step 5: Calculate the number of periods for currency depreciation
The currency depreciates at a rate of 2% every 5 years. Again, we need to consider the total time of 30 years.

To find out how many 5-year periods fit into 30 years:
\[ \text{Number of periods} = \frac{30}{5} = 6 \]

### Step 6: Calculate the depreciation factor for the currency
The depreciation factor for each 5-year period is given by:
\[ \text{Depreciation factor} = 1 - \frac{2}{100} = 0.98 \]
Thus, the total depreciation factor over 6 periods is:
\[ \text{Total depreciation factor} = (0.98)^6 \]

### Step 7: Calculate the total depreciation
Calculating \( (0.98)^6 \):
\[ (0.98)^6 \approx 0.886384 \]

### Step 8: Calculate the final value of the land
Now, we can find the final value of the land considering both appreciation and depreciation:
\[ \text{Final value} = \text{Appreciated value} \times \text{Total depreciation factor} \]
\[ \text{Final value} = 1276.28 \times 0.886384 \approx 1131.36 \text{ Rs/m²} \]

### Conclusion
The approximate value of the land per square meter 25 years hence is Rs. 1131.36.

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