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Appreciation and Appreciation and DepreciationDepreciation
Appreciation and Appreciation and DepreciationDepreciation
Appreciation Appreciation refers to an refers to an amount amount increasing.increasing.
Appreciation and Appreciation and DepreciationDepreciation
Appreciation and Appreciation and DepreciationDepreciation
Depreciation Depreciation refers to an refers to an amount amount decreasing.decreasing.
We often refer to We often refer to appreciation and appreciation and depreciation when depreciation when discussing discussing percentagespercentages
For example, if a house For example, if a house appreciates in value by appreciates in value by 6% each year, then its 6% each year, then its value increases by 6% value increases by 6% each year.each year.
On the other hand, if a On the other hand, if a car depreciates in value car depreciates in value by 10% each year, then by 10% each year, then its value decreases by its value decreases by 10% each year.10% each year.
Example of an Example of an appreciation appreciation questionquestion
Jojo purchases a new Jojo purchases a new house for $215000. house for $215000. She expects it to She expects it to appreciate in value by appreciate in value by 8% each year. 8% each year.
Assuming she is right, Assuming she is right, how much will the how much will the house be worthhouse be worth
Assuming she is right, Assuming she is right, how much will the how much will the house be worthhouse be worth
a)a) 1 year from now?1 year from now?
Assuming she is right, Assuming she is right, how much will the how much will the house be worthhouse be worth
a)a) 1 year from now?1 year from now?
b)b) 2 years from now?2 years from now?
Assuming she is right, how Assuming she is right, how much will the house be much will the house be worthworth
a)a) 1 year from now?1 year from now?
b)b) 2 years from now?2 years from now?
c)c) 3 years from now?3 years from now?
a) a) 215000 x 0.08 = 215000 x 0.08 = 1720017200
a) a) 215000 x 0.08 = 17200215000 x 0.08 = 17200
Since the value is Since the value is increasing 8%, we add increasing 8%, we add 17200 to the original 17200 to the original valuevalue
215000 + 17200 = 215000 + 17200 = 232200232200
215000 + 17200 = 215000 + 17200 = 232200232200
Therefore, the house Therefore, the house is worth $232200 after is worth $232200 after 1 year.1 year.
b) b) 232200 x 0.08 = 232200 x 0.08 = 1857618576
b) b) 232200 x 0.08 = 18576232200 x 0.08 = 18576
Since the value is Since the value is increasing 8%, we increasing 8%, we add 18576 add 18576
232200 + 18576 = 232200 + 18576 = 250576250576
232200 + 18576 = 232200 + 18576 = 250576250576
Therefore, the house Therefore, the house is worth $250576 after is worth $250576 after 2 years.2 years.
c) c) 250576 x 0.08 = 250576 x 0.08 = 20046.0820046.08
c) c) 250576 x 0.08 = 250576 x 0.08 = 20046.0820046.08
Since the value is Since the value is increasing 8%, we add increasing 8%, we add 20046.08 20046.08
250576 + 20046.08 250576 + 20046.08 = 270622.08= 270622.08
250576 + 20046.08 = 250576 + 20046.08 = 270622.08270622.08
Therefore, the house Therefore, the house is worth $270622.08 is worth $270622.08 after 3 years.after 3 years.
Example of a Example of a Depreciation Depreciation Question Question
Example: Jojo’s car Example: Jojo’s car is worth $10000 is worth $10000 today, but it will today, but it will depreciate by 12% depreciate by 12% each year. each year.
How much will the How much will the car be worth:car be worth:
How much will the How much will the car be worth:car be worth:a)a)1 year from today?1 year from today?
How much will the How much will the car be worth:car be worth:a)a)1 year from today?1 year from today?
b)b) 2 years from today?2 years from today?
How much will the car How much will the car be worth:be worth:a)a)1 year from today?1 year from today?
b)b) 2 years from today?2 years from today?
c)c) 3 years from today?3 years from today?
a) 10000 x 0.12 = a) 10000 x 0.12 = 12001200
a) 10000 x 0.12 = 1200a) 10000 x 0.12 = 1200
Since the value is Since the value is decreasing 12%, we decreasing 12%, we subtract 1200 from the subtract 1200 from the original valueoriginal value
10000 – 1200 = 10000 – 1200 = 88008800
10000 – 1200 = 880010000 – 1200 = 8800
Therefore, the car is Therefore, the car is worth $8800 after 1 worth $8800 after 1 year.year.
b) 8800 x 0.12 = 1056b) 8800 x 0.12 = 1056
b) 8800 x 0.12 = 1056b) 8800 x 0.12 = 1056
Since the value is Since the value is decreasing 12%, decreasing 12%, we subtract 1056 we subtract 1056
8800 – 1056 = 77448800 – 1056 = 7744
8800 – 1056 = 77448800 – 1056 = 7744
Therefore, the car Therefore, the car is worth $7744 is worth $7744 after 2 years. after 2 years.
c) 7744 x 0.12 = c) 7744 x 0.12 = 929.28929.28
c) 7744 x 0.12 = 929.28c) 7744 x 0.12 = 929.28
Since the value is Since the value is decreasing 12%, we decreasing 12%, we subtract 929.28subtract 929.28
7744 – 929.28 = 7744 – 929.28 = 6814.726814.72
7744 – 929.28 = 6814.727744 – 929.28 = 6814.72
Therefore, the car is Therefore, the car is worth $6814.72 after 3 worth $6814.72 after 3 years. years.
Is there an Is there an easier way to easier way to do this?do this?
Yes Yes there there is, is, JohnnyJohnny
We simply need to We simply need to convert the percentage convert the percentage that we are appreciating that we are appreciating or depreciating to a or depreciating to a decimal.decimal.
Then, if it’s an Then, if it’s an appreciation question, we appreciation question, we add that quantity to 1 to add that quantity to 1 to give us our multiplier (i.e., give us our multiplier (i.e., the base of the exponent).the base of the exponent).
On the other hand, if it’s a On the other hand, if it’s a depreciation question, we depreciation question, we subtract from 1 to give us subtract from 1 to give us our multiplier (i.e., the our multiplier (i.e., the base of the exponent).base of the exponent).
Then, we use a formula Then, we use a formula similar to the formula similar to the formula that we used for that we used for compound interest and compound interest and for half-lives.for half-lives.
For example, go back to our For example, go back to our question about Jojo and her question about Jojo and her house. It is originally worth house. It is originally worth $215000. This is the “prior” $215000. This is the “prior” amount, P.amount, P.
We are increasing the We are increasing the value by 8%. So, we value by 8%. So, we convert 8% to a decimal, convert 8% to a decimal, then add it to 1 (since it’s then add it to 1 (since it’s an appreciation question)an appreciation question)
We are increasing the We are increasing the value by 8%. So, we value by 8%. So, we convert 8% to a decimal, convert 8% to a decimal, then add it to 1then add it to 1
1 + .08 = 1.081 + .08 = 1.08
We are increasing the value We are increasing the value by 8%. So, we convert 8% by 8%. So, we convert 8% to a decimal, then add it to 1to a decimal, then add it to 1
1 + .08 = 1.081 + .08 = 1.08
This is our multiplierThis is our multiplier
11
After 1 year:After 1 year:
A = P (1.08)A = P (1.08)
11
After 1 year:After 1 year:
A = 215000 (1.08)A = 215000 (1.08)
After 1 year:After 1 year:
A = 215000 A = 215000 (1.08)(1.08)
After 1 year:After 1 year:
A = 232200A = 232200
22
After 2 years:After 2 years:
A = P (1.08)A = P (1.08)
22
After 2 years:After 2 years:
A = 215000 A = 215000 (1.08)(1.08)
After 2 years:After 2 years:
A = 215000 A = 215000 (1.1664)(1.1664)
After 2 years:After 2 years:
A = 250776A = 250776
33
After 3 years:After 3 years:
A = P (1.08)A = P (1.08)
33
After 3 years:After 3 years:
A = 215000 A = 215000 (1.08)(1.08)
After 3 years:After 3 years:
A = 215000 A = 215000 (1.259712)(1.259712)
After 3 years:After 3 years:
A = 270838.08A = 270838.08
This method allows us to This method allows us to cut right to the answer cut right to the answer and not have to figure and not have to figure out out EVERYEVERY year leading year leading up to our answerup to our answer
For example, when we were For example, when we were discussing the value of discussing the value of Jojo’s car, we calculated Jojo’s car, we calculated that after 3 years, its value that after 3 years, its value would have decreased to would have decreased to $6814.72$6814.72
We can calculate this We can calculate this a lot quicker as a lot quicker as followsfollows
We can calculate this a We can calculate this a lot quicker as followslot quicker as follows
We know that it is We know that it is depreciating by 12%depreciating by 12%
We convert 12% to a We convert 12% to a decimaldecimal
We convert 12% to a We convert 12% to a decimaldecimal
12% = 0.1212% = 0.12
Then, we subtract that Then, we subtract that amount from 1 to get amount from 1 to get our multiplier our multiplier (since it’s (since it’s a depreciation question)a depreciation question)
Then, we subtract that Then, we subtract that amount from 1 to get our amount from 1 to get our multiplier multiplier (since it’s a (since it’s a depreciation question)depreciation question)
1 – 0.12 = 0.881 – 0.12 = 0.88
33
After 3 years:After 3 years:
A = P (0.88)A = P (0.88)
33
After 3 years:After 3 years:
A = 10000 A = 10000 (0.88)(0.88)
After 3 years:After 3 years:
A = 10000 A = 10000 (0.681472)(0.681472)
After 3 years:After 3 years:
A = 6814.72A = 6814.72
After 3 years:After 3 years:
A = 6814.72A = 6814.72
Therefore, after 3 years the Therefore, after 3 years the car is worth $6814.72car is worth $6814.72
Final note about Final note about these questions!!!these questions!!!
Please note that the Please note that the question does not have question does not have to say “appreciate” or to say “appreciate” or “depreciate”. “depreciate”.
Other terms such as Other terms such as “increase”, or “decrease”, “increase”, or “decrease”, or “gain value”, or or “gain value”, or “decline” may be used, as “decline” may be used, as well as others.well as others.