Depreciation
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Question 1 of 4
1. Question
A television set with an original price of $1750 depreciates in value by 9% per year over 8 years. Solve for the following values:Round your answer to two decimal places-
New price (A):$ (822.94)Depreciation Amount (Dep):$ (927.06)
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Depreciation Formula
A=P(1−R)nDepreciation Amount
Dep=P−AFirst, summarise the data and draw a diagram for easier understanding of the problemOriginal amount (P)=$1750Depreciation rate (R)=9%(0.09)Depreciation time (n)=8 yearsNew amount (A)=?Substitute the known values into the depreciation formula to solve for the new amount.Use the decimal value of the percentage.A = P(1−R)n A = 1750(1−0.09)8 Substitute known values = 1750×0.4702525 = $822.94 Rounded to two decimal places Finally, subtract the new amount from the original amount to get the depreciation amount.Dep = P−A Dep = 1750−822.94 = $927.06 A=$822.94Dep=$927.06 -
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Question 2 of 4
2. Question
A truck with an original price of $190,000 depreciates in value by 15% per year over 5 years. Solve for the following values:Round the new amount to two decimal placesRound the depreciation amount to a whole number-
New price (A):$ (84304.01)Depreciation Amount (Dep):$ (105696)
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Depreciation Formula
A=P(1−R)nDepreciation Amount
Dep=P−AFirst, summarise the data and draw a diagram for easier understanding of the problemOriginal amount (P)=$190,000Depreciation rate (R)=15%(0.15)Depreciation time (n)=5 yearsNew amount (A)=?Substitute the known values into the depreciation formula to solve for the new amount.Use the decimal value of the percentage.A = P(1−R)n A = 190,000(1−0.15)5 Substitute known values = 190,000×(0.85)5 = 190,000×0.4437053 = $84,304.01 Rounded to two decimal places Finally, subtract the new amount from the original amount to get the depreciation amount.Dep = P−A Dep = 190,000−84,304.01 = $105,696 Rounded to a whole number A=$84,304.01Dep=$105,696 -
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Question 3 of 4
3. Question
An off-road vehicle depreciates in value by 14% per year. After 3 years, its new price is now $27,300. What was its original price?Round your answer to a whole number- Original price = (42921)
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Depreciation Formula
A=P(1−R)nDepreciation Amount
Dep=P−AFirst, summarise the data and draw a diagram for easier understanding of the problemNew amount (A)=$27,300Depreciation rate (R)=14%(0.14)Depreciation time (n)=3 yearsOriginal price (P)=?Substitute the known values into the depreciation formula to solve for the new amount.Use the decimal value of the percentage.A = P(1−R)n 27,300 = P(1−0.14)3 Substitute known values 27,300 = P×(0.86)3 27,300÷(0.86)3 = P×(0.86)3÷(0.86)3 Divide both sides by (0.86)3 27,3000.636056 = P 42,920.75 = P P = $42,921 Rounded to a whole number Original price=$42,921 -
Question 4 of 4
4. Question
If a computer with a value of $1550 depreciates at 8% per year, how many years will it take for its price to drop to $865?- (7) years
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Depreciation Formula
A=P(1−R)nDepreciation Amount
Dep=P−AFirst, summarise the data and draw a diagram for easier understanding of the problemOriginal amount (P)=$1550Depreciation rate (R)=8%(0.08)New amount (A)=$865Depreciation time (n)=?Substitute the known values into the depreciation formula to solve for the depreciation time.Use the decimal value of the percentage.A = P(1−R)n 865 = 1550(1−0.08)n Substitute known values 865 = 1550×(0.92)n 865÷1550 = 1550×(0.92)n÷1550 Divide both sides by 1550 8651550 = (0.92)n 0.558 = (0.92)n Rounded to three decimal places Finally, use trial and error by substituting values to n to which will make the left and right sides equal.Start by substituting n=6 and n=7.n=60.558 = (0.92)n 0.558 = (0.92)6 Substitute n=6 0.558 = 0.606355001344 0.558 = 0.606 Rounded to three decimal places n=70.558 = (0.92)n 0.558 = (0.92)7 Substitute n=7 0.558 = 0.55784660123648 0.558 = 0.558 Rounded to three decimal places Substituting n=7 makes the left and right sides of the equation equal.Therefore, it will take 7 years for the computer’s price to drop to $8657 years
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