Let's determine the future value of the land given that it increases at the rate of 20% per annum. The present value of the land is Rs. 10,00,000, and we need to find the value after 3 years.
We will use the compound interest formula for this calculation. The formula for compound interest is:
[tex]\[ \text{Future Value} = \text{Present Value} \times (1 + r)^n \][/tex]
where:
- [tex]\(\text{Future Value}\)[/tex] is the value we need to find,
- [tex]\(\text{Present Value} = 10,00,000 \text{ Rs}\)[/tex],
- [tex]\(r\)[/tex] is the rate of increase per annum (20% or 0.20),
- [tex]\(n\)[/tex] is the number of years (3 years).
Let's plug in the values:
[tex]\[ \text{Future Value} = 10,00,000 \times (1 + 0.20)^3 \][/tex]
First, calculate [tex]\( (1 + 0.20) \)[/tex]:
[tex]\[ 1 + 0.20 = 1.20 \][/tex]
Next, raise this to the power of 3:
[tex]\[ 1.20^3 = 1.20 \times 1.20 \times 1.20 = 1.728 \][/tex]
Finally, multiply by the present value of the land:
[tex]\[ \text{Future Value} = 10,00,000 \times 1.728 = 17,28,000 \text{ Rs} \][/tex]
Therefore, the value of the land after 3 years will be Rs. 17,28,000.
The correct answer is:
[tex]\[ \text{D} \, \text{(Rs. 17,28,000)} \][/tex]
