imported>Doug Williamson |
imported>Administrator |
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| Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.
| | ''Funds transfer''. |
| | Real-time transmission, processing or settlement. |
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| It is often denoted by a lower case (r).
| | == See also == |
| | * [[Real-time transmission, processing or settlement]] |
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| ===<span style="color:#4B0082">Example 1: Periodic yield (r) of 3%</span>===
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| GBP 1 million is borrowed or invested.
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| GBP 1.03 million is repayable at the end of the period.
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| The periodic yield (r) is:
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| r = (End amount / Start amount) - 1
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| Which can also be expressed as:
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| r = (End / Start) - 1
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| ''or''
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| r = <math>\frac{End}{Start}</math> - 1
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| = <math>\frac{1.03}{1}</math> - 1
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| = 0.03
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| = '''3%'''
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| ===<span style="color:#4B0082">Example 2: Periodic yield of 3.09%</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 yield (r) is:
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| r = <math>\frac{End}{Start}</math> - 1
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| = <math>\frac{1.00}{0.97}</math> - 1
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| = 0.030928
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| = '''3.0928%'''
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| ''Check:''
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| Amount at end = 0.97 x 1.030928 = 1.00, as expected.
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| ===<span style="color:#4B0082">Example 3: End amount from periodic yield</span>===
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| GBP 0.97 million is invested.
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| The periodic yield is 3.0928%.
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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 yield (r) is defined as:
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| r = <math>\frac{End}{Start}</math> - 1
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| ''Rearranging this relationship:''
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| 1 + r = <math>\frac{End}{Start}</math>
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| End = Start x (1 + r)
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| ''Substituting the given information into this relationship:''
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| End = GBP 0.97m x (1 + 0.030928)
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| = '''GBP 1.00m'''
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| ===<span style="color:#4B0082">Example 4: Start amount from periodic yield</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 yield is 3.0928%.
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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 yield (r) is defined as:
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| r = <math>\frac{End}{Start}</math> - 1
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| ''Rearranging this relationship:''
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| 1 + r = <math>\frac{End}{Start}</math>
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| Start = <math>\frac{End}{(1 + r)}</math>
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| ''Substitute the given data into this relationship:''
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| Start = <math>\frac{1.00}{(1 + 0.030928)}</math>
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| = '''GBP 0.97m'''
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| ''Check:''
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| Amount at start = 0.97 x 1.030928 = 1.00, as expected.
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| ===Effective annual rate (EAR)===
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| The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
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| ===Conversion formulae (r to EAR and EAR to r)===
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| EAR = (1 + r)<sup>n</sup> - 1
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| r = (1 + EAR)<sup>(1/n)</sup> - 1
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| ''Where:''
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| EAR = effective annual rate or yield
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| r = periodic interest rate or yield, as before
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| n = number of times the period fits into a calendar year
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| ===Periodic discount rate (d)===
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| The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
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| ===Conversion formulae (r to d and d to r)===
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| d = r / (1 + r)
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| r = d / (1 - d)
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| ''Where:''
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| d = periodic discount rate
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| r = periodic interest rate or yield
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| ==See also==
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| *[[Effective annual rate]]
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| *[[Discount rate]]
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| *[[Nominal annual rate]]
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| *[[Nominal annual yield]]
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| *[[Periodic discount rate]]
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| *[[Yield]]
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| *[[Forward yield]]
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| *[[Zero coupon yield]]
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| *[[Par yield]]
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| ==Other resources==
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| [[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]
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