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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) What does [tex]P \left(1+\frac{R}{100}\right)^{T} - P[/tex] indicate as per usual notation? [1 K]

(b) What will be the price of the land at the end of 2022? [2A]

(c) How much loss will there be to the person if the price decreased by [tex]$5 \%$[/tex] instead of decreasing by [tex]$4 \%$[/tex] in 2022 AD? [2HA]

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

Sagot :

GinnyAnswer
### विस्तृत समाधान (Detailed Solution):

#### (a) [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?)

गो पहाडी गणितमा, [tex]\( P \left(1 + \frac{R}{100}\right)^{T} - P \)[/tex] ले नगदको चालू शून्य बिन्दु देखि बढ़्दो ब्याजदरको अवधारणासम्म संकेत गर्छ। यसमा:

- [tex]\( P \)[/tex] मुख्य रकम हो।
- [tex]\( R \)[/tex] ब्याजदर (सालिकर) हो।
- [tex]\( T \)[/tex] समयावधि हो।

यो एउटा ब्याजदरको अवधारणा हो जहाँ मूल रकम [tex]\( P \)[/tex] समय [tex]\( T \)[/tex] को लागि ब्याज दर [tex]\( R \)[/tex] को साथ संचित गरिन्छ र यस अवधारणा मार्फत प्राप्त रकमबाट मूल रकम घटाउँदा प्राप्त रकम ब्याज हो। यसले ब्याजलाई संकेत गर्दछ जुन समयसँग संगठित हुन्छ।

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

तपाईंले पुरानो मूल्य र वृद्धि तथा घट्ने प्रक्रियालाई क्रमशः पालना गर्नुपर्नेछ। सर्वप्रथम,

2020 को अन्त्यमा मूल्य: रु. 60,00,000

2021 को सुरुमै मूल्य वृद्धि (10%):
[tex]\[ \text{वृद्धि पछि मूल्य} = 60,00,000 \times (1 + \frac{10}{100}) = 60,00,000 \times 1.1 = 66,00,000 \text{रु।} \][/tex]

2022 को अन्त्यमा मूल्य कमी (4%):
[tex]\[ \text{कमी पछि मूल्य} = 66,00,000 \times (1 - \frac{4}{100}) = 66,00,000 \times 0.96 = 63,36,000 \text{रु।} \][/tex]

#### (c) साँच्चै 2022 को अन्त्यमा 5% ले घटेको भए मानिसलाई कति घाटा हुन्छ? (How much loss will there be to the person if the price decreased by 5% instead of decreasing by 4% in 2022 AD?)

5% ले घटेको भएको मूल्य:
[tex]\[ \text{कमी पछि मूल्य (5%):} = 66,00,000 \times (1 - \frac{5}{100}) = 66,00,000 \times 0.95 = 62,70,000 \text{रु।} \][/tex]

घाटा कति भयो भन्ने मूल्यांकन:
[tex]\[ \text{घाटा} = (\text{4% कमी हुँदा मूल्य} - \text{5% कमी हुँदा मूल्य}) \][/tex]
[tex]\[ \text{घाटा} = 63,36,000 - 62,70,000 = 66,000 \text{रु।} \][/tex]

#### उत्तर:

(a) [tex]\( P \left(1 + \frac{R}{100}\right)^{T} - P \)[/tex] ले ब्याज रकमलाई सङ्केत गर्दछ जुन मूल राशि P समय अवधिमा R% ब्याज दरसँग संचित हुन्छ।

(b) 2022 को अन्त्यमा घडेरीको मूल्य रु. 63,36,000 हुनेछ।

(c) यदि 2022 मा 4% को सट्टा 5% ले घटेको भए, जग्गा बेत्न जीवन्तले रु. 66,000 घाटा हुन्छ।
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