SOLUTION: The value of a property declines every year by 5%. Presently, its value is $350,000. What will be its value 4 years from now?

Question 562480: The value of a property declines every year by 5%. Presently, its value is $350,000. What will be its value 4 years from now?
Found 2 solutions by stanbon, Sarpi:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The value of a property declines every year by 5%. Presently, its value is $350,000. What will be its value 4 years from now?
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end of 1st year: 0.95*350,000
end of 2nd year: 0.95^2*350,000
end of 3rd year: 0.95^3*350,000
end of 4th year: 0.95^4*350,000 = 285077.19
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Cheers,
Stan H.
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Answer by Sarpi(32) (Show Source): You can put this solution on YOUR website!
Value of a Property.
Let the timing be: t = 0,1,2,3,4,5 (in years)
Value at t=0 is $350,000
Depreciation rate = 5%
Therefore what will be value at t=4?
Long calculation:
0; 350,000
1; 350,000 - (350,000*5%) = 332,500
2; 332,500 - (332,500*5%) = 315,875
3; 315,875 - (315,875*5%) = 300,081.25
4; 300,081.25 - (300,081.25*5%) = 285,077.1875
5; 285077.1875-(285077.1875 *5%) = 270,823.3281

Short Calculation (using the compounding formula)
Amount = Principal(1+Rate)^time
so here; principal is the initial value = $350,000
Rate is a declining rate, so -5%
time = 4yrs
A = 350,000 * (1-5%)^4
A = 350,000 * (0.95)^4
A = 285,077.1875
Hence the value 4 years from now will be $285,077.19 (rounded to 2 decimal)

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