1.Seven years ago,Rocco's drum kit cost him R12500. It has now been valued at R2300.what rate of simple depreciation does this represent?
2.Fiona buys a DStv satellite dish for R3000.Due to weathering,its value depreciates simply at 15% p.a. After how long will the satellite dish have a book value of zero?
if it depreciates at r% per year, then
12500(1-r/100)^7 = 2300
r = 21.5%
the book value will never be zero. No matter how many times you multiply by 0.85 the answer is never zero. Presumably at some small fraction of residual value the book value is zero, but that has not been stated.
Thank u Steve
1. To calculate the rate of simple depreciation, we can use the formula:
(Initial value - Current value) / (Initial value) * 100
Substituting the given values, we have:
(12500 - 2300) / 12500 * 100 = 9200 / 12500 * 100 = 73.6
Therefore, the rate of simple depreciation for Rocco's drum kit is 73.6%.
2. To determine the time it takes for the satellite dish to have a book value of zero, we need to find when the value depreciates to zero.
Using the formula for simple depreciation, we can calculate the time (t):
Book value = Initial value - (Depreciation rate * Initial value * t)
0 = 3000 - (0.15 * 3000 * t)
Dividing both sides of the equation by 3000:
0 = 1 - 0.15t
0.15t = 1
t = 1 / 0.15 = 6.67 (approximately)
Therefore, the satellite dish will have a book value of zero after approximately 6.67 years.
To find the rate of simple depreciation in question 1, you would use the following formula:
Depreciation = (Initial Value - Current Value) / Number of Years
In this case, the initial value is R12500, and the current value is R2300. The number of years is 7.
Depreciation = (12500 - 2300) / 7 = 10200 / 7 = 1457.14
Therefore, the rate of simple depreciation is R1457.14 per year.
For question 2, to determine how long it will take for the satellite dish to have a book value of zero, you need to calculate the number of years it will take for the depreciation to accumulate to the total initial value.
Let's assume X is the number of years it will take.
Depreciation = Initial Value * Depreciation Rate * Number of Years
In this case, the initial value is R3000, and the depreciation rate is 15% per year.
Depreciation = 3000 * 0.15 * X
Since we want the book value to be zero, we can set up the following equation:
0 = 3000 - (3000 * 0.15 * X)
Simplifying the equation:
0 = 3000 - 450X
Rearranging the equation:
450X = 3000
X = 3000 / 450
X = 6.67 years
Therefore, the satellite dish will have a book value of zero after approximately 6.67 years.