example 2 Depreciation Chapter 8.4 An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on. a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%. b. Find the yearly depreciation and show that the sum of the depreciations is $24,000. 2009 PBLPathways
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Example 2 Depreciation Chapter 8.4 An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years- digits depreciation method. Under.
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example 2 Depreciation
Chapter 8.4
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
2009 PBLPathways
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
sum of the five years' digits 1 2 3 4 5 15
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
sum of the five years' digits 1 2 3 4 5 15
5 4 3 2 1, , , ,
15 15 15 15 15
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
sum of the five years' digits 1 2 3 4 5 15
5 4 3 2 1, , , ,
15 15 15 15 15
1 1 55
5 15
5 15 151
2 2 2n
n
n a a a as s
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
sum of the five years' digits 1 2 3 4 5 15
5 4 3 2 1, , , ,
15 15 15 15 15
1 1 55
5 15
5 15 151
2 2 2n
n
n a a a as s
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
a. Write a sequence that represents the parts of the automobile value that are depreciated in each year, and show that the sum of the terms is 100%.
sum of the five years' digits 1 2 3 4 5 15
5 4 3 2 1, , , ,
15 15 15 15 15
1 1 55
5 15
5 15 151
2 2 2n
n
n a a a as s
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
Year Depreciation
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
Year Depreciation
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
Year Depreciation
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
Year Depreciation
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
n an
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
n an
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
n an
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.
n an
1 900,000
2 870,000
3 840,000
4 810,000
5
515 24,000 or 8000
415 24,000 or 6400
315 24,000 or 4800
215 24,000 or 3200
115 24,000 or 1600
1
1 55
2
5
2
5 8000 1600
2
24,000
nn
n a as
a as
2009 PBLPathways
An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years-digits depreciation method. Under this method, annual depreciation is found by multiplying the value of the property by a fraction whose denominator is the sum of the 5 years’ digits and whose numerator is 5 for the first year’s depreciation, 4 for the second year’s, 3 for the third, and so on.
b. Find the yearly depreciation and show that the sum of the depreciations is $24,000.