David bought a new car for shilling 800,000. After 5 years, he sold it through a second-hand car dealer. The dealer charged a commission of 4% for the sale of the car. If David received shilling 480,000, calculate the annual rate of depreciation of the car.
(800000*r^5)(.96) = 480000
r = .91
So, the car depreciated at 9% per year
To calculate the annual rate of depreciation of the car, we need to determine the difference between the purchase price and the selling price, and then divide that difference by the number of years.
1. First, calculate the commission charged by the second-hand car dealer: commission = 4% * selling price
In this case, the selling price is 480,000 shillings, so the commission will be: commission = 4% * 480,000 = 0.04 * 480,000 = 19,200 shillings.
2. Next, determine the selling price before the commission was deducted: selling price before commission = selling price + commission
In this case, the selling price before the commission deduction will be: selling price before commission = 480,000 + 19,200 = 499,200 shillings.
3. Now, calculate the difference between the purchase price and the selling price before the commission deduction: depreciation = purchase price - selling price before commission
In this case, the purchase price is 800,000 shillings, so the depreciation will be: depreciation = 800,000 - 499,200 = 300,800 shillings.
4. Finally, divide the depreciation by the number of years to get the annual rate of depreciation: annual rate of depreciation = depreciation / number of years
Since the car was sold after 5 years, the annual rate of depreciation will be: annual rate of depreciation = 300,800 / 5 = 60,160 shillings per year.
Therefore, the annual rate of depreciation of the car is 60,160 shillings per year.