Periodic yield
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
or
r = (End / Start) -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 / Start) - 1
= (1.00 / 0.97) - 1
= 0.030928
= 3.0928%
Check:
0.97 x 1.030928 = 1.00.
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 / 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
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 / Start) - 1
Rearranging this relationship:
1 + r = End / Start
Start = End / (1 + r)
Substitute the given data into this relationship:
Start = GBP 1.00m / (1 + 0.030928)
= GBP 0.97m
Check:
0.97 x 1.030928 = 1.00, as expected.
