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(Create page. Sources: linked pages, Techopedia webpage https://www.techopedia.com/definition/1564/paypal and PayPal webpage https://www.paypal.com/uk/webapps/mpp/paypal-popup)
 
imported>Doug Williamson
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''Payments''.
Periodic discount rate is a cost of borrowing - or rate of return - expressed as:


PayPal is an online service that allows individuals to make payments through PayPal as an intermediary, without sharing financial information with the recipient.
*The excess of the amount at the end over the amount at the start
*Divided by the amount at the end




== See also ==
==Calculating periodic discount rate from start and end cash==


* [[Direct debit]]
Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic discount rate.
* [[Fintech]]
* [[Payments and payment systems]]
* [[Request to Pay]]
* [[Ripple payment protocol]]
* [[Strong Customer Authentication]]
* [[Track and trace]]


[[Category:Accounting,_tax_and_regulation]]
 
[[Category:The_business_context]]
<span style="color:#4B0082">'''Example 1: Discount rate of 2.91%'''</span>
[[Category:Identify_and_assess_risks]]
 
[[Category:Manage_risks]]
GBP 1 million is borrowed.
[[Category:Risk_frameworks]]
 
[[Category:Cash_management]]
GBP 1.03 million is repayable at the end of the period.
[[Category:Financial_products_and_markets]]
 
[[Category:Liquidity_management]]
 
The periodic discount rate (d) is:
 
d = (End amount - Start amount) / End amount
 
Which can also be expressed as:
 
d = (End - Start) / End
 
= (1.03 - 1) / 1.03
 
= 0.029126
 
= '''2.9126%'''
 
 
<span style="color:#4B0082">'''Example 2: Discount rate of 3%'''</span>
 
GBP 0.97 million is borrowed or invested
 
GBP 1.00 million is repayable at the end of the period.
 
 
The periodic discount rate (d) is:
 
= (End - Start) / End
 
 
= (1.00 - 0.97) / 1.00
 
= 0.030000
 
= '''3.0000%'''
 
 
==Calculating end cash from periodic discount rate==
 
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 discount rate, we can calculate the end amount.
 
 
<span style="color:#4B0082">'''Example 3: End amount from periodic discount rate'''</span>
 
GBP  0.97 million is borrowed.
 
The periodic discount rate is 3.0000%.
 
Calculate the amount repayable at the end of the period.
 
 
'''''Solution'''''
 
The periodic discount rate (d) is:
 
d = (End - Start) / End
 
 
d = (End / End) - (Start / End)
 
 
d = 1 - (Start / End)
 
 
''Rearranging this relationship:''
 
1 - d = (Start / End)
 
 
End = Start / (1 - d)
 
 
''Substituting the given information into this relationship:''
 
End = 0.97 / (1 - 0.030000)
 
 
= 0.97 / 0.97
 
 
= '''GBP 1.00m'''
 
 
==Calculating start cash from periodic discount rate==
 
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 discount rate, we can calculate the start amount.
 
 
<span style="color:#4B0082">'''Example 4: Start amount from periodic discount rate'''</span>
 
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
 
The periodic discount rate is 3.0000%.
 
Calculate the amount invested at the start of the period.
 
 
'''''Solution'''''
 
As before, the periodic discount rate (d) is defined as:
 
d = (End - Start) / End
 
 
d = 1 - (Start / End)
 
 
''Rearranging this relationship:''
 
(Start / End) = 1 - d
 
 
Start = End x (1 - d)
 
 
''Substitute the given data into this relationship:''
 
Start = 1.00 x (1 - 0.030000)
 
= '''GBP 0.97m'''
 
 
==Periodic yield==
 
The periodic discount rate (d) is also related to the [[periodic yield]] (r), and each can be calculated from the other.
 
 
====Conversion formulae (d to r and r to d)====
 
r = d / (1 - d)
 
d = r / (1 + r)
 
 
''Where:''
 
r = periodic interest rate or yield
 
d = periodic discount rate
 
 
 
==See also==
 
*[[Effective annual rate]]
*[[Certificate in Treasury Fundamentals]]
*[[Certificate in Treasury]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Periodic yield]]
*[[Yield]]
 
[[Category:Corporate_finance]]

Latest revision as of 12:03, 22 February 2018

Periodic discount rate is a cost of borrowing - or rate of return - expressed as:

  • The excess of the amount at the end over the amount at the start
  • Divided by the amount at the end


Calculating periodic discount rate from start and end cash

Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic discount rate.


Example 1: Discount rate of 2.91%

GBP 1 million is borrowed.

GBP 1.03 million is repayable at the end of the period.


The periodic discount rate (d) is:

d = (End amount - Start amount) / End amount

Which can also be expressed as:

d = (End - Start) / End

= (1.03 - 1) / 1.03

= 0.029126

= 2.9126%


Example 2: Discount rate of 3%

GBP 0.97 million is borrowed or invested

GBP 1.00 million is repayable at the end of the period.


The periodic discount rate (d) is:

= (End - Start) / End


= (1.00 - 0.97) / 1.00

= 0.030000

= 3.0000%


Calculating end cash from periodic discount rate

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 discount rate, we can calculate the end amount.


Example 3: End amount from periodic discount rate

GBP 0.97 million is borrowed.

The periodic discount rate is 3.0000%.

Calculate the amount repayable at the end of the period.


Solution

The periodic discount rate (d) is:

d = (End - Start) / End


d = (End / End) - (Start / End)


d = 1 - (Start / End)


Rearranging this relationship:

1 - d = (Start / End)


End = Start / (1 - d)


Substituting the given information into this relationship:

End = 0.97 / (1 - 0.030000)


= 0.97 / 0.97


= GBP 1.00m


Calculating start cash from periodic discount rate

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 discount rate, we can calculate the start amount.


Example 4: Start amount from periodic discount rate

An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.

The periodic discount rate is 3.0000%.

Calculate the amount invested at the start of the period.


Solution

As before, the periodic discount rate (d) is defined as:

d = (End - Start) / End


d = 1 - (Start / End)


Rearranging this relationship:

(Start / End) = 1 - d


Start = End x (1 - d)


Substitute the given data into this relationship:

Start = 1.00 x (1 - 0.030000)

= GBP 0.97m


Periodic yield

The periodic discount rate (d) is also related to the periodic yield (r), and each can be calculated from the other.


Conversion formulae (d to r and r to d)

r = d / (1 - d)

d = r / (1 + r)


Where:

r = periodic interest rate or yield

d = periodic discount rate


See also