The formula to calculate the Zero Coupon Bond Effective Yield (ZCB Yield) is:
\[ ZCB Yield = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1 \]
Where:
Zero Coupon Bond Effective Yield is used to calculate the periodic return for a zero coupon bond, or sometimes referred to as a discount bond.
Face Value is the nominal value or dollar value of a security stated by the issuer.
Present Value of the annuity is the value that determines the value of a series of future periodic payments at a given time.
Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.
Let's assume the following values:
Using the formula:
\[ ZCB Yield = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1 \]
Evaluating:
\[ ZCB Yield = \left( \frac{800}{9} \right)^{\frac{1}{2}} - 1 \]
The Zero Coupon Bond Effective Yield is 8.42809041582063.
| Face Value | Present Value | Number of Periods | Zero Coupon Bond Effective Yield |
|---|---|---|---|
| 700 | 9 | 2 | 7.81917103688197 |
| 800 | 9 | 2 | 8.42809041582063 |
| 900 | 9 | 2 | 9.00000000000000 |
| 1000 | 9 | 2 | 9.54092553389460 |
| 1100 | 9 | 2 | 10.05541596785133 |
| 1200 | 9 | 2 | 10.54700538379252 |
| 1300 | 9 | 2 | 11.01850425154663 |
| 1400 | 9 | 2 | 11.47219128924647 |
| 1500 | 9 | 2 | 11.90994448735806 |