Respuesta :
At the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
What is appreciation and deprecation?
Deprecation, also called devaluation, is the decrement in price of an asset. Appreciation is opposite of deprecation. This indicates increment in the price of the considered thing.
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
It is given that:
- Initial price of the plot of land = $350,000
- First year: 12% appreciation
- Second year: 10% appreciation
- Third year: 8% devaluation
- Fourth year: 6% appreciation
Now, consider appreciation of an amount A by P%.
Then, we have:
Increased price = Initial price + P% of initial price
Increased price = [tex]A + \dfrac{A}{100} \times P = A \times \left(1 + \dfrac{P}{100} \right)[/tex]
Similarly, depreciated price by P% of an amount A is:
Decreased price = [tex]A - \dfrac{A}{100} \times P = A \times \left(1 - \dfrac{P}{100} \right)[/tex]
We've got: A = 350,000
After 1st year, which had 12% appreciation, we get:
[tex]A_1 =A(1 + 12/100) = A(1.12)\\[/tex]
After 2nd year, 10% appreciation we get:
[tex]A_2 =A_1(1 + 10/100) = A_1(1.1) = A(1.12)(1.1)\\[/tex]
After 3rd year, which had 8% devaluation effect on the price, we get:
[tex]A_3 = A_2(1 - 8/100) = A_2(1-0.08) = A_2(0.92) = A(1.12)(1.1)(0.92)[/tex]
After 4th year, which had 6% appreciation effect on the price, we get:[tex]A_4 = A_3(1 + 6/100) = A_4(1+0.06) = A_3(1.06) = A(1.12)(1.1)(0.92)(1.06)[/tex]
Thus, the final effect on A is:
[tex]A \rightarrow A(1.12)(1.1)(0.92)(1.06) = A(1.2014464)\\\$350,000 \rightarrow 350000(1.2014464) = 420506.24\: \rm dollars[/tex]
Thus, at the end of the analyzed period this plot of land will have the value as given by: Option D: 420,506.24
Learn more about percent here:
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