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Question 1 of 4
A television set with an original price of $1750$1750 depreciates in value by 9%9% per year over 88 years. Solve for the following values:
Round your answer to two decimal places
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First, summarise the data and draw a diagram for easier understanding of the problem
Original amount (P)=$1750
Depreciation rate (R)=9%(0.09)
Depreciation time (n)=8 years
New 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 |
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Question 2 of 4
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 places
Round the depreciation amount to a whole number
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First, summarise the data and draw a diagram for easier understanding of the problem
Original amount (P)=$190,000
Depreciation rate (R)=15%(0.15)
Depreciation time (n)=5 years
New 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=$84,304.01
Dep=$105,696
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Question 3 of 4
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
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First, summarise the data and draw a diagram for easier understanding of the problem
New amount (A)=$27,300
Depreciation rate (R)=14%(0.14)
Depreciation time (n)=3 years
Original 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 |
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Question 4 of 4
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?
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First, summarise the data and draw a diagram for easier understanding of the problem
Original amount (P)=$1550
Depreciation rate (R)=8%(0.08)
New amount (A)=$865
Depreciation 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=6
0.558 |
= |
(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=7
0.558 |
= |
(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 $865