Periodic discount rate
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
or
d = (End - Start) / End
= (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 - Start) / End
= (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 - Start) / End
d = (End / End) - (Start / End)
d = 1 - (Start / End)
Rearranging this relationship:
(Start / End) = 1 - d
Start = End x (1 - d)
Start / (1 - d) = End
End = Start / (1 - d)
Substituting the given information into this relationship:
End = 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 - 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 = GBP 1.00m x (1 - 0.030000)
= GBP 0.97m
