NACT and Periodic discount rate: Difference between pages

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''US''.
__NOTOC__
A cost of borrowing - or rate of return - expressed as:


National Association of Corporate Treasurers.
*The excess of the amount at the end over the amount at the start
*Divided by the amount at the end




== See also ==
==Example 1==
* [[Association of Corporate Treasurers]]
GBP 1 million is borrowed.
* [[EACT]]
 
* [[IGTA]]
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
 
= (1.03 - 1) / 1.03
 
= 0.029126
 
= '''2.9126%'''
 
 
==Example 2==
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 amount - start amount) / End amount
 
= (1.00 - 0.97) /  1.00
 
= 0.030000
 
= '''3.0000%'''
 
 
==Example 3==
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 defined as:
 
d = (End amount - start amount) / End amount
 
d = 1 - (Start amount / End amount)
 
 
''Rearranging this relationship:''
 
(Start amount / End amount) = 1 - d
 
Start amount = End amount x (1 - d)
 
Start amount / (1 - d) = End amount
 
End amount = Start amount / (1 - d)
 
 
''Substituting the given information into this relationship:''
 
End amount = GBP 0.97m / (1 - 0.030000)
 
= GBP 0.97m / 0.97
 
= '''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 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 amount - start amount) / End amount
 
d = 1 - (Start amount / End amount)
 
 
''Rearranging this relationship:''
 
(Start amount / End amount) = 1 - d
 
Start amount = End amount x (1 - d)
 
 
''Substitute the given data into this relationship:''
 
Start amount = GBP 1.00m x (1 - 0.030000)
 
= '''GBP 0.97m'''
 
 
 
==See also==
 
*[[Effective annual rate]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Periodic yield]]
*[[Yield]]

Revision as of 15:04, 26 October 2015

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


Example 1

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

= (1.03 - 1) / 1.03

= 0.029126

= 2.9126%


Example 2

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 amount - start amount) / End amount

= (1.00 - 0.97) / 1.00

= 0.030000

= 3.0000%


Example 3

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 defined as:

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

d = 1 - (Start amount / End amount)


Rearranging this relationship:

(Start amount / End amount) = 1 - d

Start amount = End amount x (1 - d)

Start amount / (1 - d) = End amount

End amount = Start amount / (1 - d)


Substituting the given information into this relationship:

End amount = GBP 0.97m / (1 - 0.030000)

= GBP 0.97m / 0.97

= 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 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 amount - start amount) / End amount

d = 1 - (Start amount / End amount)


Rearranging this relationship:

(Start amount / End amount) = 1 - d

Start amount = End amount x (1 - d)


Substitute the given data into this relationship:

Start amount = GBP 1.00m x (1 - 0.030000)

= GBP 0.97m


See also