Periodic yield: Difference between revisions
imported>Doug Williamson (Expand example) |
imported>Doug Williamson (Additional explanation) |
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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. | |||
==Example 1== | ====Example 1==== | ||
GBP 1 million is borrowed or invested. | GBP 1 million is borrowed or invested. | ||
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r = (End amount / start amount) - 1 | r = (End amount / start amount) - 1 | ||
Which can also be expressed as: | |||
r = (End / Start) -1 | r = (End / Start) - 1 | ||
''or'' | |||
= | r = <math>\frac{End}{Start}</math> - 1 | ||
= <math>\frac{1.03}{1}</math> - 1 | |||
= 0.03 | = 0.03 | ||
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==Example 2== | ====Example 2==== | ||
GBP 0.97 million is borrowed or invested. | GBP 0.97 million is borrowed or invested. | ||
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The periodic yield (r) is: | The periodic yield (r) is: | ||
r = <math>\frac{End}{Start}</math> - 1 | |||
= | = <math>\frac{1.00}{0.97}</math> - 1 | ||
= 0.030928 | = 0.030928 | ||
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''Check:'' | ''Check:'' | ||
0.97 x 1.030928 = 1.00. | Amount at end = 0.97 x 1.030928 = 1.00, as expected. | ||
==Example 3== | ====Example 3==== | ||
GBP 0.97 million is invested. | GBP 0.97 million is invested. | ||
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Calculate the amount repayable at the end of the period. | Calculate the amount repayable at the end of the period. | ||
'''''Solution''''' | |||
The periodic yield (r) is defined as: | The periodic yield (r) is defined as: | ||
r = | r = <math>\frac{End}{Start}</math> - 1 | ||
''Rearranging this relationship:'' | ''Rearranging this relationship:'' | ||
1 + r = End / | 1 + r = <math>\frac{End}{Start}</math> | ||
End = Start x (1 + r) | End = Start x (1 + r) | ||
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==Example 4== | ====Example 4==== | ||
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period. | An investment will pay out a single amount of GBP 1.00m at its final maturity after one period. | ||
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Calculate the amount invested at the start of the period. | Calculate the amount invested at the start of the period. | ||
'''''Solution''''' | |||
As before, the periodic yield (r) is defined as: | As before, the periodic yield (r) is defined as: | ||
r = | r = <math>\frac{End}{Start}</math> - 1 | ||
''Rearranging this relationship:'' | ''Rearranging this relationship:'' | ||
1 + r = End / | 1 + r = <math>\frac{End}{Start}</math> | ||
Start = End | Start = <math>\frac{End}{(1 + r)}</math> | ||
''Substitute the given data into this relationship:'' | ''Substitute the given data into this relationship:'' | ||
Start = | Start = <math>\frac{1.00}{(1 + 0.030928)}</math> | ||
= '''GBP 0.97m''' | = '''GBP 0.97m''' | ||
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''Check:'' | ''Check:'' | ||
0.97 x 1.030928 = 1.00, as expected. | Amount at start = 0.97 x 1.030928 = 1.00, as expected. | ||
====Effective annual rate==== | |||
The Periodic yield (r) is related to the [[Effective annual rate]] (EAR), and each can be calculated from the other. | |||
Revision as of 12:12, 28 October 2015
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.
Example 1
GBP 1 million is borrowed or invested.
GBP 1.03 million is repayable at the end of the period.
The periodic yield (r) is:
r = (End amount / start amount) - 1
Which can also be expressed as:
r = (End / Start) - 1
or
r = <math>\frac{End}{Start}</math> - 1
= <math>\frac{1.03}{1}</math> - 1
= 0.03
= 3%
Example 2
GBP 0.97 million is borrowed or invested.
GBP 1.00 million is repayable at the end of the period.
The periodic yield (r) is:
r = <math>\frac{End}{Start}</math> - 1
= <math>\frac{1.00}{0.97}</math> - 1
= 0.030928
= 3.0928%
Check:
Amount at end = 0.97 x 1.030928 = 1.00, as expected.
Example 3
GBP 0.97 million is invested.
The periodic yield is 3.0928%.
Calculate the amount repayable at the end of the period.
Solution
The periodic yield (r) is defined as:
r = <math>\frac{End}{Start}</math> - 1
Rearranging this relationship:
1 + r = <math>\frac{End}{Start}</math>
End = Start x (1 + r)
Substituting the given information into this relationship:
End = GBP 0.97m x (1 + 0.030928)
= GBP 1.00m
Example 4
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
The periodic yield is 3.0928%.
Calculate the amount invested at the start of the period.
Solution
As before, the periodic yield (r) is defined as:
r = <math>\frac{End}{Start}</math> - 1
Rearranging this relationship:
1 + r = <math>\frac{End}{Start}</math>
Start = <math>\frac{End}{(1 + r)}</math>
Substitute the given data into this relationship:
Start = <math>\frac{1.00}{(1 + 0.030928)}</math>
= GBP 0.97m
Check:
Amount at start = 0.97 x 1.030928 = 1.00, as expected.
Effective annual rate
The Periodic yield (r) is related to the Effective annual rate (EAR), and each can be calculated from the other.
