Question:
Mr. Durani bought a plot of land for 180000 and a car for 3320000 at the same time. The value of the plot of land grows uniformly at the rate of 30% pa.. while the value of the car depreciates by 20% in the first year and by 15% p.a. thereafter. If he sells the plot of land as well as the car after 3 years, what will be his profit or loss?
Solution:
To calculate Durani’s profit or loss when selling the plot of land and the car after 3 years, we need to consider the change in their values over this period.
- The value of the plot of land grows at a rate of 30% per annum. To find the value after 3 years, we can use the formula for compound interest:
Future Value = Present Value * (1 + Rate)^Time
Present Value (PV) = 180,000 Rate (R) = 30% per annum or 0.30 Time (T) = 3 years
Future Value = 180,000 * (1 + 0.30)^3 Future Value = 180,000 * (1.30)^3 Future Value = 180,000 * 2.197
Future Value of the plot of land after 3 years = 395,460
- The value of the car depreciates by 20% in the first year and by 15% per annum thereafter. To find the value after 3 years, we can calculate the depreciated value each year:
Year 1: Value = 3,320,000 – (20% of 3,320,000) Year 1 Value = 3,320,000 – 0.20 * 3,320,000 Year 1 Value = 3,320,000 – 664,000 Year 1 Value = 2,656,000
Year 2: Value = 2,656,000 – (15% of 2,656,000) Year 2 Value = 2,656,000 – 0.15 * 2,656,000 Year 2 Value = 2,656,000 – 398,400 Year 2 Value = 2,257,600
Year 3: Value = 2,257,600 – (15% of 2,257,600) Year 3 Value = 2,257,600 – 0.15 * 2,257,600 Year 3 Value = 2,257,600 – 338,640 Year 3 Value = 1,918,960
The car’s value after 3 years is 1,918,960.
Now, to calculate Durani’s profit or loss, subtract the total cost of the car and plot of land from their total selling value:
Total Cost = Cost of land + Cost of car Total Cost = 180,000 + 3,320,000 Total Cost = 3,500,000
Total Selling Value = Value of land + Value of car after 3 years Total Selling Value = 395,460 + 1,918,960 Total Selling Value = 2,314,420
Profit or Loss = Total Selling Value – Total Cost Profit or Loss = 2,314,420 – 3,500,000 Profit or Loss = -1,185,580
Durani will incur a loss of 1,185,580 when selling the plot of land and the car after 3 years.