Depreciation and Profit/Loss

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3. Depreciation and Profit/Loss

a) The formula to find compound depreciation is:

V_t = P\left(1 - \frac{R}{100}\right)^t

where $V_t$ is the value after $t$ years, $P$ is the original value, $R$ is the depreciation rate, and $t$ is the time in years.

b) To find the selling price of the truck after 3 years:

Identify the given values.
Original cost of truck ( $P$ ) = NRs. 40,00,000
Depreciation rate ( $R$ ) = 15% p.a.
Time ( $t$ ) = 3 years
Apply the compound depreciation formula.
$V_t = P\left(1 - \frac{R}{100}\right)^t$ $V_3 = 40,00,000\left(1 - \frac{15}{100}\right)^3$ $V_3 = 40,00,000(1 - 0.15)^3$ $V_3 = 40,00,000(0.85)^3$ $V_3 = 40,00,000 \times 0.614125$ $V_3 = 24,56,500$
The selling price of the truck after 3 years is NRs. 24,56,500.

c) To find the profit or loss percent to the businessman:
Calculate the total money spent by the businessman.
Total money spent = Original cost of truck = NRs. 40,00,000
Calculate the total money received by the businessman.
Money received from selling the truck = NRs. 24,56,500 (from part b)
Earnings from using the truck = NRs. 9,07,000
Total money received = NRs. 24,56,500 + NRs. 9,07,000 = NRs. 33,63,500
Calculate the net profit or loss.
Net Profit/Loss = Total money received - Total money spent
Net Profit/Loss = NRs. 33,63,500 - NRs. 40,00,000
Net Profit/Loss = -NRs. 6,36,500
Since the value is negative, it is a loss.
Loss = NRs. 6,36,500
Calculate the loss percentage.
$\text{Loss Percentage} = \frac{\text{Loss}}{\text{Original Cost}} \times 100\%$ $\text{Loss Percentage} = \frac{6,36,500}{40,00,000} \times 100\%$ $\text{Loss Percentage} = 0.159125 \times 100\%$ $\text{Loss Percentage} = 15.9125\%$
The businessman incurred a loss of \boxed{\text{15.9125%}}.

4. Currency Exchange

a) A currency exchange rate is the value of one country's currency in terms of another country's currency. It indicates how much of one currency can be exchanged for a unit of another currency.

b) To find how many American dollars Pemba will get for NRs. 2,15,160:
Identify the relevant exchange rate.
Pemba is exchanging Nepali Rupees for American Dollars, meaning the bank is selling USD to Pemba.
Bank's selling rate for 1 USD = NRs. 143.44
Calculate the amount of USD Pemba receives.
$\text{Amount in USD} = \frac{\text{Total NRs}}{\text{Selling rate}}$ $\text{Amount in USD} = \frac{2,15,160}{143.44}$ $\text{Amount in USD} = 1500$
Pemba will get $\boxed{\text{1500 American dollars}}$ .

c) To find how many Nepali rupees Pemba will get back after exchanging the American dollars on the same day:
Identify the relevant exchange rate.
Pemba now has USD and wants to convert them back to NRs, meaning the bank is buying USD from Pemba.
Bank's buying rate for 1 USD = NRs. 142.84
Calculate the amount of NRs Pemba receives.
Amount of USD Pemba has = 1500 USD (from part b)
$\text{Amount in NRs} = \text{Amount in USD} \times \text{Buying rate}$ $\text{Amount in NRs} = 1500 \times 142.84$ $\text{Amount in NRs} = 2,14,260$
Pemba will get back $\boxed{\text{NRs. 2,14,260}}$ .

Depreciation and Profit/Loss

Step-by-step solution

Identify the given values.

Apply the compound depreciation formula.

Calculate the total money spent by the businessman.

Calculate the total money received by the businessman.

Calculate the net profit or loss.

Calculate the loss percentage.

Identify the relevant exchange rate.

Calculate the amount of USD Pemba receives.

Identify the relevant exchange rate.

Calculate the amount of NRs Pemba receives.

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