00:01
In this question, the given part is, the declining balance method is an accounting method in which the amount of depreciation taken each year is a fixed percentage of the present value of the item.
00:15
If y is the value of the item in a given year, the depreciation taken is a multiplied by y for some depreciation rate a with a is greater than 0 and less than 1.
00:26
And the new value is 1 minus a multiplied by y.
00:30
This question consists of two parts.
00:34
We will start with part a.
00:43
In this part, if the initial value of the item is y node, then we need to show that the value of the nes of depreciation is 1 minus a to the power n, 1 minus a to the power n, multiplied by y note.
01:09
Denote the value after i years of depreciation.
01:34
Then yn equals to 1 minus a multiplied by yn minus 1...