Periodic yield and SLA: Difference between pages

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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.  
Service Level Agreement.


It is often denoted by a lower case (r).


== See also ==
* [[QA]]
* [[Service level agreement]]
* [[SLA partner banking]]


==Calculating periodic yield from start and end cash==
[[Category:Compliance_and_audit]]
Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic yield.
 
 
<span style="color:#4B0082">'''Example 1: Periodic yield (r) of 3%'''</span>
 
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
 
= (1.03 / 1.00) - 1
 
= 0.03
 
= '''3%'''
 
 
<span style="color:#4B0082">'''Example 2: Periodic yield of 3.09%'''</span>
 
GBP  0.97 million is borrowed or invested.
 
GBP 1.00 million is repayable at the end of the period.
 
 
As before, the periodic yield (r) is:
 
r = (End / Start) - 1
 
= (1.00 / 0.97) - 1
 
= 0.030928
 
= '''3.0928%'''
 
 
''Check:''
 
Amount at end = 0.97 x 1.030928 = GBP 1.00m, as expected.
 
 
==Calculating end cash from periodic yield==
We can also work this relationship in the other direction.
 
Given the cash amount at the start of an investment or borrowing period, together with the periodic yield, we can calculate the end amount.
 
 
<span style="color:#4B0082">'''Example 3: End amount from periodic yield'''</span>
 
GBP  0.97 million is invested.
 
The periodic yield is 3.0928%.
 
Calculate the amount repayable at the end of the period.
 
 
'''''Solution'''''
 
As before, the periodic yield (r) is:
 
r = (End / Start) - 1
 
 
''Rearranging this relationship:''
 
1 + r = (End / Start)
 
 
End = Start x (1 + r)
 
 
''Substituting the given information into this relationship:''
 
End = GBP 0.97m x (1 + 0.030928)
 
= '''GBP 1.00m'''
 
 
==Calculating start cash from periodic yield==
We can also work the same relationship reversing the direction of time travel.
 
Given the cash amount at the end of an investment or borrowing period, again together with the periodic yield, we can calculate the start amount.
 
 
<span style="color:#4B0082">'''Example 4: Start amount from periodic yield'''</span>
 
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:
 
r = (End / Start) - 1
 
 
 
''Rearranging this relationship:''
 
1 + r = (End / Start)
 
 
Start = End / (1 + r)
 
 
''Substitute the given data into this relationship:''
 
Start = End / (1 + 0.030928)
 
 
= '''GBP 0.97m'''
 
 
''Check:''
 
Amount at end = 0.97 x 1.030928 = GBP 1.00m, as expected.
 
 
==Effective annual rate (EAR)==
 
The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
 
 
====Conversion formulae (r to EAR and EAR to r)====
 
EAR = (1 + r)<sup>n</sup> - 1
 
r = (1 + EAR)<sup>(1/n)</sup> - 1
 
 
''Where:''
 
EAR = effective annual rate or yield
 
r = periodic interest rate or yield, as before
 
n = number of times the period fits into a calendar year
 
 
==Periodic discount rate (d)==
 
The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
 
 
====Conversion formulae (r to d and d to r)====
 
d = r / (1 + r)
 
r = d / (1 - d)
 
 
''Where:''
 
d = periodic discount rate
 
r = periodic interest rate or yield
 
 
==See also==
 
*[[Discount rate]]
*[[Effective annual rate]]
*[[Forward yield]]
*[[Nominal annual rate]]
*[[Nominal annual yield]]
*[[Par yield]]
*[[Periodic discount rate]]
*[[Yield]]
*[[Zero coupon yield]]
 
 
== Other resources ==
[[Media:2016_02_Feb_-_Many_happy_returns.pdf| Many happy returns - calculating and applying interest rates and yields, The Treasurer]]
 
[[Media:2013_09_Sept_-_Simple_solutions.pdf| Simple solutions - converting between yields, The Treasurer]]
 
[[Category:Corporate_financial_management]]
[[Category:Cash_management]]

Revision as of 14:17, 2 May 2018

Service Level Agreement.


See also