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Questions and Answers
What is the defining characteristic of simple depreciation?
What is the defining characteristic of simple depreciation?
- Depreciation is calculated on the remaining book value each year.
- The depreciation amount decreases each year.
- The book value of the asset never reaches zero.
- Depreciation is a fixed percentage of the initial principal amount. (correct)
Using simple depreciation, if an asset initially valued at $P$ depreciates at a rate of $i$ per year, what is its book value ($A$) after $n$ years?
Using simple depreciation, if an asset initially valued at $P$ depreciates at a rate of $i$ per year, what is its book value ($A$) after $n$ years?
- $A = P(1 - i)^n$
- $A = P(1 + i)^n$
- $A = P(1 - in)$ (correct)
- $A = P(1 + in)$
Which method of depreciation results in a decreasing depreciation amount each year?
Which method of depreciation results in a decreasing depreciation amount each year?
- Straight-line depreciation
- Compound depreciation (correct)
- Fixed depreciation
- Simple depreciation
An item initially valued at $10,000 depreciates using simple depreciation at a rate of 10% per year. What is its book value after 3 years?
An item initially valued at $10,000 depreciates using simple depreciation at a rate of 10% per year. What is its book value after 3 years?
For compound depreciation, if $P$ is the initial value and $i$ is the depreciation rate, the book value $A$ after $n$ years is given by:
For compound depreciation, if $P$ is the initial value and $i$ is the depreciation rate, the book value $A$ after $n$ years is given by:
An asset valued at $5,000 is depreciated using compound depreciation at a rate of 20% per year. What is its approximate book value after 2 years?
An asset valued at $5,000 is depreciated using compound depreciation at a rate of 20% per year. What is its approximate book value after 2 years?
What is the primary purpose of using timelines in financial calculations?
What is the primary purpose of using timelines in financial calculations?
If interest is compounded quarterly, what is the value of 'p' in the compound interest formula $A = P(1 + \frac{i}{p})^{np}$?
If interest is compounded quarterly, what is the value of 'p' in the compound interest formula $A = P(1 + \frac{i}{p})^{np}$?
An investment of $2,000 is made at an annual interest rate of 8% compounded semi-annually for 3 years. What is the accumulated amount?
An investment of $2,000 is made at an annual interest rate of 8% compounded semi-annually for 3 years. What is the accumulated amount?
What is the relationship between nominal interest rate and effective interest rate when interest is compounded more than once a year?
What is the relationship between nominal interest rate and effective interest rate when interest is compounded more than once a year?
Given a nominal interest rate of 6% compounded monthly, what is the formula to calculate the effective annual interest rate ($i_{\text{effective}}$)?
Given a nominal interest rate of 6% compounded monthly, what is the formula to calculate the effective annual interest rate ($i_{\text{effective}}$)?
If the effective annual interest rate is 10%, and interest is compounded quarterly, what is the nominal annual interest rate?
If the effective annual interest rate is 10%, and interest is compounded quarterly, what is the nominal annual interest rate?
An asset is purchased for $20,000 and depreciates using simple depreciation over 5 years to a book value of $10,000. What is the annual depreciation rate?
An asset is purchased for $20,000 and depreciates using simple depreciation over 5 years to a book value of $10,000. What is the annual depreciation rate?
A machine initially costs $50,000 and is expected to depreciate to $25,000 in 4 years using compound depreciation. What is the approximate annual depreciation rate?
A machine initially costs $50,000 and is expected to depreciate to $25,000 in 4 years using compound depreciation. What is the approximate annual depreciation rate?
Consider two assets with the same initial value and the same annual depreciation rate. Asset X depreciates using simple depreciation, and Asset Y depreciates using compound depreciation. After several years, which of the following statements will be true?
Consider two assets with the same initial value and the same annual depreciation rate. Asset X depreciates using simple depreciation, and Asset Y depreciates using compound depreciation. After several years, which of the following statements will be true?
In simple depreciation, how does the depreciation amount change annually?
In simple depreciation, how does the depreciation amount change annually?
An asset is purchased for $10,000 and depreciates using simple depreciation at an annual rate of 8%. What is the book value of the asset after 5 years?
An asset is purchased for $10,000 and depreciates using simple depreciation at an annual rate of 8%. What is the book value of the asset after 5 years?
Which statement best describes the pattern of book value reduction under compound depreciation?
Which statement best describes the pattern of book value reduction under compound depreciation?
A company uses compound depreciation at a rate of 15% per year for its equipment. If a machine was initially worth $20,000, what is its approximate book value after 3 years?
A company uses compound depreciation at a rate of 15% per year for its equipment. If a machine was initially worth $20,000, what is its approximate book value after 3 years?
For an asset depreciating using compound depreciation, will the book value ever theoretically reach zero?
For an asset depreciating using compound depreciation, will the book value ever theoretically reach zero?
If an asset's book value after 4 years of simple depreciation at a 10% annual rate is $6,000, what was its original principal amount?
If an asset's book value after 4 years of simple depreciation at a 10% annual rate is $6,000, what was its original principal amount?
What is the primary benefit of using timelines in financial calculations involving compound interest?
What is the primary benefit of using timelines in financial calculations involving compound interest?
If interest is compounded monthly, what value of 'p' should be used in the compound interest formula $A = P\Bigl(1 + rac{i}{p}\Bigr)^{np}$?
If interest is compounded monthly, what value of 'p' should be used in the compound interest formula $A = P\Bigl(1 + rac{i}{p}\Bigr)^{np}$?
An investment of $5,000 is made at an annual interest rate of 6% compounded quarterly for 2 years. What is the accumulated amount? (Round to the nearest dollar)
An investment of $5,000 is made at an annual interest rate of 6% compounded quarterly for 2 years. What is the accumulated amount? (Round to the nearest dollar)
What is the relationship between the effective interest rate and the nominal interest rate when interest is compounded more frequently than annually?
What is the relationship between the effective interest rate and the nominal interest rate when interest is compounded more frequently than annually?
Given a nominal interest rate of 8% compounded semi-annually, what is the effective annual interest rate?
Given a nominal interest rate of 8% compounded semi-annually, what is the effective annual interest rate?
If the effective annual interest rate is 12%, and interest is compounded quarterly, what is the nominal annual interest rate? (Approximate to two decimal places)
If the effective annual interest rate is 12%, and interest is compounded quarterly, what is the nominal annual interest rate? (Approximate to two decimal places)
Consider two identical assets, Asset X and Asset Y, both purchased for $P$ and depreciating at the same annual rate $i$. Asset X uses simple depreciation and Asset Y uses compound depreciation. After $n$ years ($n > 1$), which asset will have a lower book value?
Consider two identical assets, Asset X and Asset Y, both purchased for $P$ and depreciating at the same annual rate $i$. Asset X uses simple depreciation and Asset Y uses compound depreciation. After $n$ years ($n > 1$), which asset will have a lower book value?
A rare painting was purchased for $200,000$. It is expected to depreciate in value using compound depreciation. After 10 years, it is valued at $120,000. What is the approximate annual compound depreciation rate?
A rare painting was purchased for $200,000$. It is expected to depreciate in value using compound depreciation. After 10 years, it is valued at $120,000. What is the approximate annual compound depreciation rate?
Which of the following scenarios would result in the highest accumulated amount after 5 years, assuming the same principal and nominal annual interest rate?
Which of the following scenarios would result in the highest accumulated amount after 5 years, assuming the same principal and nominal annual interest rate?
Under simple depreciation, which factor remains constant throughout the asset's lifespan?
Under simple depreciation, which factor remains constant throughout the asset's lifespan?
In compound depreciation, what happens to the depreciation amount as the asset ages?
In compound depreciation, what happens to the depreciation amount as the asset ages?
What is the purpose of 'p' in the compound interest formula $A = P(1 + \frac{i}{p})^{np}$?
What is the purpose of 'p' in the compound interest formula $A = P(1 + \frac{i}{p})^{np}$?
What type of decay is represented by the formula $A = P(1 - i)^n$?
What type of decay is represented by the formula $A = P(1 - i)^n$?
If an investment is compounded quarterly, how should you adjust the annual interest rate ($i$) and the number of years ($n$) in the compound interest formula?
If an investment is compounded quarterly, how should you adjust the annual interest rate ($i$) and the number of years ($n$) in the compound interest formula?
When finding the depreciation rate, what type of equation is involved in compound decay?
When finding the depreciation rate, what type of equation is involved in compound decay?
What is the relationship between the initial value ($P$), book value ($A$), depreciation rate ($i$), and time ($n$) in simple depreciation?
What is the relationship between the initial value ($P$), book value ($A$), depreciation rate ($i$), and time ($n$) in simple depreciation?
What does the effective interest rate represent?
What does the effective interest rate represent?
What is the annual interest rate of an investment of $5,000 that after two years is worth $5,618?
What is the annual interest rate of an investment of $5,000 that after two years is worth $5,618?
If a company wants to ensure that its assets reflect their true value after depreciation, which depreciation method would provide a more accurate book value over time?
If a company wants to ensure that its assets reflect their true value after depreciation, which depreciation method would provide a more accurate book value over time?
If the nominal interest rate is 8% compounded quarterly, calculate the effective annual interest rate. (Round to two decimal places)
If the nominal interest rate is 8% compounded quarterly, calculate the effective annual interest rate. (Round to two decimal places)
A company uses simple depreciation for an asset initially valued at $10,000. After 4 years, the book value is $6,000. What is the annual depreciation rate ($i$)?
A company uses simple depreciation for an asset initially valued at $10,000. After 4 years, the book value is $6,000. What is the annual depreciation rate ($i$)?
An asset is depreciating using compound depreciation at an annual rate of 10%. How many years will it take for the asset's book value to be approximately half of its original value?
An asset is depreciating using compound depreciation at an annual rate of 10%. How many years will it take for the asset's book value to be approximately half of its original value?
Consider two assets: Asset X depreciates using simple depreciation and Asset Y depreciates using compound depreciation. Both have the same initial value and the same annual depreciation rate. After a certain number of years, Asset Y's book value becomes exactly half of its original value. At that same point in time, what can be said about Asset X's remaining book value relative to its original value?
Consider two assets: Asset X depreciates using simple depreciation and Asset Y depreciates using compound depreciation. Both have the same initial value and the same annual depreciation rate. After a certain number of years, Asset Y's book value becomes exactly half of its original value. At that same point in time, what can be said about Asset X's remaining book value relative to its original value?
A rare collectible is appreciating in value at a rate that can be modeled using compound interest. Its value increases from $10,000 to $15,000 over 5 years. If you want to determine the nominal annual rate that, when compounded continuously, would yield the same growth, which of the following formulas would provide the most accurate calculation?
A rare collectible is appreciating in value at a rate that can be modeled using compound interest. Its value increases from $10,000 to $15,000 over 5 years. If you want to determine the nominal annual rate that, when compounded continuously, would yield the same growth, which of the following formulas would provide the most accurate calculation?
Flashcards
Simple Depreciation
Simple Depreciation
Reduces asset value by a constant amount yearly, based on the initial principal.
Simple Depreciation Formula
Simple Depreciation Formula
A = P(1 - in), where A is the book value, P is the principal, i is the depreciation rate, and n is time in years.
Compound Depreciation
Compound Depreciation
Depreciation calculated on the remaining asset value each year, resulting in a decreasing depreciation amount.
Compound Depreciation Formula
Compound Depreciation Formula
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Timelines (Finance)
Timelines (Finance)
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Compound Interest Formula
Compound Interest Formula
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Nominal Interest Rate
Nominal Interest Rate
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Effective Interest Rate
Effective Interest Rate
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Simple Interest Formula
Simple Interest Formula
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Compound Interest Formula
Compound Interest Formula
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Effective Interest Rate Formula
Effective Interest Rate Formula
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Nominal Interest Rate Formula
Nominal Interest Rate Formula
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What is straight-line depreciation?
What is straight-line depreciation?
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What is Book Value (Simple Depreciation)?
What is Book Value (Simple Depreciation)?
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How to calculate book value after simple depreciation
How to calculate book value after simple depreciation
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What is reducing-balance depreciation?
What is reducing-balance depreciation?
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What is Book Value (Compound Depreciation)?
What is Book Value (Compound Depreciation)?
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How to calculate book value after compound depreciation
How to calculate book value after compound depreciation
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How to find the simple depreciation rate
How to find the simple depreciation rate
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How to find the compound depreciation rate
How to find the compound depreciation rate
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Adjustments for compounding periods
Adjustments for compounding periods
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How to use Timelines
How to use Timelines
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Book Value
Book Value
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Compound Depreciation Characteristic
Compound Depreciation Characteristic
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Straight-Line Depreciation
Straight-Line Depreciation
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What is 'i'?
What is 'i'?
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What is 'P'?
What is 'P'?
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What is 'A'?
What is 'A'?
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What is 'n'?
What is 'n'?
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Why Use Timelines?
Why Use Timelines?
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Subsequent Periods
Subsequent Periods
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Study Notes
Simple Depreciation
- Simple depreciation, or straight-line depreciation, reduces an asset's value by a fixed amount annually.
- Depreciation is based on the initial principal.
- The formula for simple depreciation is: (A = P(1 - in)), where:
- (A) = Book value or depreciated value.
- (P) = Principal amount.
- (i) = Depreciation rate (as a decimal).
- (n) = Time period in years.
- The depreciation amount remains constant each year.
- Total depreciation is calculated as ( P \times i \times n ).
- The depreciated value decreases linearly over time.
Compound Depreciation
- Compound depreciation, or reducing-balance depreciation, calculates depreciation on the asset's remaining value each year.
- This results in a decreasing depreciation amount each year.
- The formula for calculating compound depreciation is: (A = P(1 - i)^n), where:
- (A) = Book value or depreciated value.
- (P) = Principal amount.
- (i) = Depreciation rate (as a decimal).
- (n) = Time period in years.
- The book value never reaches zero with compound depreciation.
- Depreciated value follows an exponential decay pattern.
Finding Depreciation Rate ((i))
- The annual depreciation rate ((i)) for simple or compound decay can be found by solving the respective depreciation formulas for (i).
- For simple decay: (A = P(1 - in)).
- For compound decay: (A = P(1 - i)^n).
- For simple decay, the relationship between initial value, final value, and depreciation rate is linear.
- For compound decay, solving for the rate involves an exponential equation.
Timelines
- Timelines help visualize compounding periods and interest rate changes over an investment or loan term.
- The interest rate and number of compounding periods should be adjusted based on the frequency of compounding (e.g., quarterly, monthly).
- When interest rates change or deposits/withdrawals occur, timelines should be broken into segments, and each period calculated separately.
- The compound interest formula is used to find the accumulated value at the end of each segment, and the principal is adjusted for the next period accordingly.
Compound Interest Formula
- The formula is: (A = P\Bigl(1 + \frac{i}{p}\Bigr)^{np}), where:
- (A) = Accumulated amount.
- (P) = Principal amount.
- (i) = Annual interest rate (as a decimal).
- (p) = Number of compounding periods per year.
- (n) = Number of years.
Calculations
- For the initial period, calculate the accumulated value using the compound interest formula.
- Adjust the principal for any deposits or withdrawals.
- For subsequent periods, recalculate the accumulated value, considering interest rate changes or transactions.
- Sum the values from each period to determine the total accumulated value.
Formulas for Interest and Depreciation
- Simple Interest: (A = P(1 + in))
- Compound Interest: (A = P(1 + i)^n)
- Simple Depreciation: (A = P(1 - in))
- Compound Depreciation: (A = P(1 - i)^n)
- Effective Interest Rate: (1 + i_{\text{effective}} = \Bigl(1 + \frac{i_{\text{nominal}}}{m}\Bigr)^m)
- Nominal Interest Rate: (i_{\text{nominal}} = m \Bigl[\bigl(1 + i_{\text{effective}}\bigr)^{\frac{1}{m}} - 1\Bigr])
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