Depreciation is the loss in value of an asset over time. Straight-line depreciation subtracts a fixed dollar amount each period; declining-balance (reducing-balance) depreciation subtracts a fixed percentage of the current value each period, so the dollar amount lost shrinks over time. An annuity is a sequence of regular, equal payments — either paid into an investment or paid off a loan — and understanding how they grow (or shrink) relies on the same compounding ideas as depreciation and compound interest.
Example
A $30,000 car depreciating by 15% per year (declining balance) loses $4,500 in year one, but only about $3,825 in year two, since 15% is taken of the smaller remaining value each time — unlike straight-line depreciation, which would lose the same dollar amount every year.
Key terms
Depreciation:
The loss in value of an asset over time.
Declining-balance depreciation:
Depreciation calculated as a fixed percentage of the current value each period.
Annuity:
A sequence of regular, equal payments made or received over time.
Questions
1. Depreciation is:
The loss in value of an asset over time
The gain in value of an asset over time
A type of loan repayment only
A fixed one-time fee
2. Straight-line depreciation subtracts:
A fixed dollar amount each period
A fixed percentage of the current value each period
Nothing at all
A random amount each period
3. Declining-balance depreciation subtracts:
A fixed percentage of the current value each period
A fixed dollar amount each period
Nothing at all
A random amount each period
4. An annuity is:
A sequence of regular, equal payments over time
A single one-time payment only
A type of car
A type of depreciation only
5. With declining-balance depreciation, the dollar amount lost each period:
Shrinks over time
Stays exactly the same every period
Grows without limit forever
Is always zero
6. A car losing value each year is an example of:
Depreciation
Appreciation
An annuity only, with no depreciation
A type of interest rate
7. Regular monthly loan repayments are an example of:
An annuity
Depreciation only
A single one-time payment
A type of asset
8. A $10,000 asset depreciating by $1,000 per year (straight-line) is worth how much after 3 years?
$7,000
$9,000
$6,000
$8,000
9. A $30,000 car depreciating 15% (declining balance) in year one loses:
$4,500
$3,000
$15,000
$1,500
10. After losing $4,500 in year one, a $30,000 car depreciating 15% (declining balance) is worth how much at the start of year two?
$25,500
$27,000
$25,000
$26,500
11. A retirement fund receiving equal monthly deposits over many years is an example of:
An annuity
Straight-line depreciation
Declining-balance depreciation only
A one-time payment
12. Why does declining-balance depreciation lose less in dollar terms each successive year, even at a fixed percentage rate?
The percentage is applied to a smaller remaining value each time, so the dollar loss shrinks
The percentage rate itself decreases automatically each year
Declining-balance depreciation always loses the exact same dollar amount every year
This method has no relationship between percentage and dollar value
13. Why might a business prefer declining-balance depreciation for tax purposes in some situations?
It reflects larger value loss earlier, which can align with how some assets actually lose value fastest when new
Depreciation method has no effect on how asset value is reported
Straight-line depreciation is always required for every type of asset
Declining-balance depreciation always produces identical results to straight-line
14. A $30,000 car depreciating 15% (declining balance) is worth approximately how much after 2 years?
$21,675
$25,500
$27,000
$19,500
15. Why is calculating the true value of an annuity more complex than simply adding up all the individual payments?
Money paid or received at different times has different value due to compounding, so timing must be accounted for
Every payment in an annuity is always worth the exact same amount regardless of timing
Annuities never involve any form of compounding or growth
Simple addition always gives the fully accurate value of an annuity
16. Why might straight-line depreciation understate an asset's early value loss compared to declining-balance for assets (like cars) that lose value fastest when new?
Straight-line spreads loss evenly, while declining-balance concentrates more loss in the earlier periods
Straight-line and declining-balance always produce identical loss patterns for any asset
Assets always lose value at a perfectly constant rate throughout their life
Declining-balance depreciation always understates early value loss, not straight-line
17. A $30,000 car depreciating 15% per year (declining balance) will be worth approximately how much after 3 years?
$18,424
$15,000
$21,675
$16,575
18. Why might understanding annuities be essential for planning retirement savings, rather than just knowing simple interest rates?
Retirement savings typically involve many regular contributions compounding together over decades, not a single lump sum
Retirement savings never involve regular or repeated contributions
Simple interest calculations fully capture how retirement savings accumulate
Annuities have no practical connection to retirement planning
19. Why might a business choosing between financing equipment with a loan (an annuity of repayments) versus paying upfront weigh the total interest paid over time?
Spreading payments over time via a loan generally costs more in total due to accumulated interest
Financing through a loan is always exactly as cheap as paying the full amount upfront
Interest never accumulates on business equipment loans specifically
Total cost is unrelated to whether payments are spread out or paid upfront
20. Why might comparing straight-line and declining-balance depreciation totals over an asset's full useful life sometimes converge, despite different early results?
Both methods ultimately account for the same total loss in value, just distributed differently across the periods
The two methods always produce a completely different total loss over the asset's full life
Depreciation methods have no defined endpoint or total value loss
Straight-line depreciation always results in a larger total loss than declining-balance
21. Why might an annuity used to save for retirement rely on the same underlying mathematics as a loan repayment annuity?
Both involve a sequence of regular, equal amounts combined with compounding growth or reduction over time
Savings annuities and loan annuities are mathematically unrelated concepts
Only loan repayments ever involve any form of compounding
Retirement savings never involve regular, equal contributions
Answer key (parent copy)
1. The loss in value of an asset over time
2. A fixed dollar amount each period
3. A fixed percentage of the current value each period
4. A sequence of regular, equal payments over time
5. Shrinks over time
6. Depreciation
7. An annuity
8. $7,000
9. $4,500
10. $25,500
11. An annuity
12. The percentage is applied to a smaller remaining value each time, so the dollar loss shrinks
13. It reflects larger value loss earlier, which can align with how some assets actually lose value fastest when new
14. $21,675
15. Money paid or received at different times has different value due to compounding, so timing must be accounted for
16. Straight-line spreads loss evenly, while declining-balance concentrates more loss in the earlier periods
17. $18,424
18. Retirement savings typically involve many regular contributions compounding together over decades, not a single lump sum
19. Spreading payments over time via a loan generally costs more in total due to accumulated interest
20. Both methods ultimately account for the same total loss in value, just distributed differently across the periods
21. Both involve a sequence of regular, equal amounts combined with compounding growth or reduction over time