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
