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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

= (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 amount / start amount) - 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 amount / start amount) - 1

Rearranging this relationship:

End amount = Start amount x (1 + r)

Substituting the given information into this relationship:

End amount = 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 amount / start amount) - 1

Rearranging this relationship:

Start amount = End amount / (1 + r)

Substitute the given data into this relationship:

Start amount = GBP 1.00m / (1 + 0.030928)

= GBP 0.97m

Check:

0.97 x 1.030928 = 1.00, as expected.

See also

• Effective annual rate
• Discount rate
• Nominal annual rate
• Periodic discount rate
• Yield