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.

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