imported>Doug Williamson |
imported>Doug Williamson |
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| Periodic discount rate is a cost of borrowing - or rate of return - expressed as:
| | A law established by an act of the legislature. |
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| *The excess of the amount at the end over the amount at the start
| | Contrasted with case law or common law, established by precedent. |
| *Divided by the amount at the end
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| ==Calculating periodic discount rate from start and end cash== | | == See also == |
| | * [[Case law]] |
| | * [[Codification]] |
| | * [[Common law]] |
| | * [[Consolidation]] |
| | * [[Eiusdem generis]] |
| | * [[Enabling Act]] |
| | * [[Legislature]] |
| | * [[Private Bill]] |
| | * [[Public Bill]] |
| | * [[Royal assent]] |
| | * [[Statutory]] |
| | * [[Statutory duty]] |
| | * [[Statutory filing]] |
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| Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic discount rate.
| | [[Category:Compliance_and_audit]] |
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| <span style="color:#4B0082">'''Example 1: Discount rate of 2.91%'''</span>
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| GBP 1 million is borrowed.
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| GBP 1.03 million is repayable at the end of the period.
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| The periodic discount rate (d) is:
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| d = (End amount - Start amount) / End amount
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| Which can also be expressed as:
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| d = (End - Start) / End
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| = (1.03 - 1) / 1.03
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| = 0.029126
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| = '''2.9126%'''
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| <span style="color:#4B0082">'''Example 2: Discount rate of 3%'''</span>
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| GBP 0.97 million is borrowed or invested
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| GBP 1.00 million is repayable at the end of the period.
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| The periodic discount rate (d) is:
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| = (End - Start) / End
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| = (1.00 - 0.97) / 1.00
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| = 0.030000
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| = '''3.0000%'''
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| ==Calculating end cash from periodic discount rate==
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| We can also work this relationship in the other direction.
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| Given the cash amount at the start of an investment or borrowing period, together with the periodic discount rate, we can calculate the end amount.
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| <span style="color:#4B0082">'''Example 3: End amount from periodic discount rate'''</span>
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| GBP 0.97 million is borrowed.
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| The periodic discount rate is 3.0000%.
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| Calculate the amount repayable at the end of the period.
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| '''''Solution'''''
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| The periodic discount rate (d) is:
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| d = (End - Start) / End
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| d = (End / End) - (Start / End)
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| d = 1 - (Start / End)
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| ''Rearranging this relationship:''
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| 1 - d = (Start / End)
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| End = Start / (1 - d)
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| ''Substituting the given information into this relationship:''
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| End = 0.97 / (1 - 0.030000)
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| = 0.97 / 0.97
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| = '''GBP 1.00m'''
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| ==Calculating start cash from periodic discount rate==
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| We can also work the same relationship reversing the direction of time travel.
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| Given the cash amount at the end of an investment or borrowing period, again together with the periodic discount rate, we can calculate the start amount.
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| <span style="color:#4B0082">'''Example 4: Start amount from periodic discount rate'''</span>
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| An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
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| The periodic discount rate is 3.0000%.
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| Calculate the amount invested at the start of the period.
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| '''''Solution'''''
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| As before, the periodic discount rate (d) is defined as:
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| d = (End - Start) / End
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| d = 1 - (Start / End)
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| ''Rearranging this relationship:''
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| (Start / End) = 1 - d
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| Start = End x (1 - d)
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| ''Substitute the given data into this relationship:''
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| Start = 1.00 x (1 - 0.030000)
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| = '''GBP 0.97m'''
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| ==Periodic yield==
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| The periodic discount rate (d) is also related to the [[periodic yield]] (r), and each can be calculated from the other.
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| ====Conversion formulae (d to r and r to d)====
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| r = d / (1 - d)
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| d = r / (1 + r)
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| ''Where:''
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| r = periodic interest rate or yield
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| d = periodic discount rate
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| ==See also==
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| *[[Effective annual rate]]
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| *[[Certificate in Treasury Fundamentals]]
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| *[[Certificate in Treasury]]
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| *[[Discount rate]]
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| *[[Nominal annual rate]]
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| *[[Periodic yield]]
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| *[[Yield]]
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