The price of a piece of land in Kathmandu was fixed at Rs [tex]$60,00,000$[/tex] at the end of 2020 AD. The price increased by [tex]$10\%$[/tex] as a consequence of increasing buying pressure at the beginning of 2021. However, the price of land decreased by [tex][tex]$4\%$[/tex][/tex] due to the economic crisis at the end of 2022 AD.

(a) चलन चल्तीको संकेतअनुसार [tex]$P \left(1+\frac{ R }{100}\right)^{ T }- P$[/tex] ले के जनाउँछ?
(What does [tex]$P \left(1+\frac{ R }{100}\right)^{ T }- P$[/tex] indicate as per usual notation?)

(b) 2022 को अन्त्यमा सो घडेरीको मूल्य कति भयो होला, पत्ता लगाउनुहोस्।
(What will be the price of the land at the end of 2022?)

(c) ई.सं. 2022 मा [tex][tex]$4\%$[/tex][/tex] ले घटनुको साटो [tex]$5\%$[/tex] ले घटेको भए जग्गा बेच्ने मानिसलाई कति घाटा हुन्थ्यो होला, गणना गरी पत्ता लगाउनुहोस्।
(How much loss would there be to the person if the price decreased by [tex]$5\%$[/tex] instead of decreasing by [tex][tex]$4\%$[/tex][/tex] in 2022 AD?)

Answers:
(a) Growth
(b) Rs [tex]$63,36,000$[/tex]
(c) Rs [tex]$66,000$[/tex] loss

Let's go through the problem step-by-step.

Given:
- The initial price of a piece of land in Kathmandu at the end of 2020 was Rs 60,00,000.
- The price increased by 10% at the beginning of 2021.
- The price decreased by 4% at the end of 2022.

(a) चलन चल्तीको सइकेतअनुसार [tex]$ P \left(1 + \frac{R}{100}\right)^T - P $[/tex] ले के जनाउँछ ? (What does [tex]$ P \left(1 + \frac{R}{100}\right)^T - P $[/tex] as per the usual notation indicate?)

The expression [tex]$ P \left(1 + \frac{R}{100}\right)^T - P $[/tex] represents the growth of the initial price [tex]$ P $[/tex] over [tex]$ T $[/tex] years at a rate of [tex]$ R \% $[/tex]. This formula indicates how much the price has increased (or decreased) over a specified period at a given percentage rate. The term [tex]$ P \left(1 + \frac{R}{100}\right)^T $[/tex] represents the new price after the increase/decrease, and subtracting the initial price [tex]$ P $[/tex] gives the total change in price.

Result:
The expression indicates "Growth".

(b) 2022 को अन्त्यमा सो घडेरीको मूल्य कति भयो होला, पत्ता लगाउनुहोस् । (What will be the price of the land at the end of 2022?)

To calculate the price at the end of 2022:
1. First, calculate the price at the beginning of 2021 after a 10% increase.
2. Then, calculate the price at the end of 2022 after a 4% decrease.

1. Calculate the price at the beginning of 2021:
[tex]\[ \text{Price in 2021} = \text{Initial Price} \times \left(1 + \frac{10}{100}\right) \][/tex]
[tex]\[ \text{Price in 2021} = 60,00,000 \times 1.10 = 66,00,000 \text{ Rs} \][/tex]

2. Calculate the price at the end of 2022:
[tex]\[ \text{Price in 2022} = \text{Price in 2021} \times \left(1 - \frac{4}{100}\right) \][/tex]
[tex]\[ \text{Price in 2022} = 66,00,000 \times 0.96 \approx 63,36,000 \text{ Rs} \][/tex]

Result:
The price of the land at the end of 2022 would be Rs 63,36,000.

(c) ई.सं. 2022 मा [tex]$ 4 \% $[/tex] ले घटनुको साटो [tex]$ 5 \% $[/tex] ले घटेको भए जग्गा बेच्ने मानिसलाई कति घाटा हुन्थ्यो होला, गणना गरी पत्ता लगाउनुहोस् । (How much loss will be there to the person if the price decreased by 5% instead of 4% in 2022 AD?)

To calculate the loss if the price decreased by 5% instead of 4%:
1. Calculate the hypothetical price at the end of 2022 if the decrease was 5%.

[tex]\[ \text{Hypothetical Price in 2022} = \text{Price in 2021} \times \left(1 - \frac{5}{100}\right) \][/tex]
[tex]\[ \text{Hypothetical Price} = 66,00,000 \times 0.95 = 62,70,000 \text{ Rs} \][/tex]

2. Determine the loss by subtracting the hypothetical price from the calculated price after a 4% decrease.

[tex]\[ \text{Loss} = \text{Price after 4% decrease} - \text{Hypothetical Price} \][/tex]
[tex]\[ \text{Loss} = 63,36,000 - 62,70,000 = 66,000 \text{ Rs} \][/tex]

Result:
The loss would be Rs 66,000.

Final Answers:
(a) Growth
(b) Rs 63,36,000
(c) Rs 66,000 loss