The cost of a minibus was Shilling 950,000. It depreciated in value by 5% per year for the first two years by 15% per year for the subsequent years.
(a) Calculate the value of the minibus after years
(b) After 5 years the minibus was sold through a dealer at 25% more than its value to Mr. X. If the dealers’ sale price was to be taken as its value after depreciation, calculate the average monthly rate of depreciation for 5 years.
To calculate the value of the minibus after a certain number of years, we need to apply the depreciation percentages for each year. Let's break it down step by step:
(a) Calculate the value of the minibus after years:
Step 1: Calculate the value after the first two years of 5% depreciation per year.
The minibus depreciates by 5% per year for the first two years, so we need to calculate the value after 2 years.
Value after 1st year = 950,000 - (5% of 950,000)
Value after 1st year = 950,000 - 47,500
Value after 1st year = 902,500
Value after 2nd year = 902,500 - (5% of 902,500)
Value after 2nd year = 902,500 - 45,125
Value after 2nd year = 857,375
Step 2: Calculate the value after subsequent years of 15% depreciation per year.
The minibus depreciates by 15% per year for the subsequent years. Let's assume the minibus is owned for 'n' years after the initial two years.
Value after the 2nd year = 857,375
Value after the 3rd year = 857,375 - (15% of 857,375)
Value after the 4th year = Value after the 3rd year - (15% of Value after the 3rd year)
Value after the 5th year = Value after the 4th year - (15% of Value after the 4th year)
And so on...
You can continue this pattern until you reach the desired number of years.
(b) Calculate the average monthly rate of depreciation for 5 years:
To calculate the average monthly rate of depreciation, we need to find the difference between the initial value of the minibus and the selling price after 5 years. Then, we divide this difference by the number of months in 5 years.
Difference in value = Selling price - Initial value
The selling price is given as 25% more than the value after depreciation, which we calculated above.
Average monthly rate of depreciation = (Difference in value) / (Number of months in 5 years)
I hope this explanation helps you in solving the problem.