Periodic yield: Difference between revisions
imported>Doug Williamson (Link with Nominal annual rate page.) |
imported>Doug Williamson (Expand examples) |
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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. | 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. | ||
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The periodic yield (r) is: | The periodic yield (r) is: | ||
(End amount / start amount) - 1 | r = (End amount / start amount) - 1 | ||
= (1.03 / 1) - 1 | = (1.03 / 1) - 1 | ||
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= 0.03 | = 0.03 | ||
= 3% | = '''3%''' | ||
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= 0.030928 | = 0.030928 | ||
= 3.0928% | = '''3.0928%''' | ||
==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 = (End amount / start amount) - 1 | |||
Rearranging this relationship: | |||
End amount = Start amount x (1 + r) | |||
Substituting the given information into this relationship: | |||
End amount = 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 = (End amount / start amount) - 1 | |||
Rearranging this relationship: | |||
Start amount = End amount / (1 + r) | |||
Substitute the given data into this relationship: | |||
Start amount = GBP 1.00m / (1 + 0.030928) | |||
= '''GBP 0.97m''' | |||
Check: | |||
0.97 x 1.030928 | |||
= 1.00, as expected. | |||
Revision as of 14:47, 26 October 2015
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
= (1.03 / 1) - 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:
(End amount / start amount) - 1
= (1.00 / 0.97) - 1
= 0.030928
= 3.0928%
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 = (End amount / start amount) - 1
Rearranging this relationship:
End amount = Start amount x (1 + r)
Substituting the given information into this relationship:
End amount = 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 = (End amount / start amount) - 1
Rearranging this relationship:
Start amount = End amount / (1 + r)
Substitute the given data into this relationship:
Start amount = GBP 1.00m / (1 + 0.030928)
= GBP 0.97m
Check:
0.97 x 1.030928
= 1.00, as expected.
