The formula to calculate the Zero Coupon Bond Value (V) is:
\[ V = \frac{FV}{(1 + \frac{RoR}{100})^T} \]
Where:
Zero Coupon Bond Value is referred to as a pure discount bond or simply discount bond, is a bond that does not pay coupon payments, and instead pays one lump sum at maturity.
Face Value is the nominal value or dollar value of a security stated by the issuer.
A Rate of Return is the gain or loss on an investment over a specified time period, expressed as a percentage of the investment’s cost.
Time to Maturity is the time required to mature a bond.
Let's assume the following values:
Using the formula:
\[ V = \frac{FV}{(1 + \frac{RoR}{100})^T} \]
Evaluating:
\[ V = \frac{800}{(1 + \frac{4}{100})^{11}} \]
The Zero Coupon Bond Value is 519.664745250614.
| Face Value | Rate of Return | Time to Maturity | Zero Coupon Bond Value |
|---|---|---|---|
| 700 | 3% | 10 years | 520.865740427707465 |
| 700 | 3% | 11 years | 505.694893619133438 |
| 700 | 3% | 12 years | 490.965916135080988 |
| 700 | 3.5% | 10 years | 496.243169596840517 |
| 700 | 3.5% | 11 years | 479.461999610473924 |
| 700 | 3.5% | 12 years | 463.248308802390284 |
| 700 | 4% | 10 years | 472.894918178059072 |
| 700 | 4% | 11 years | 454.706652094287506 |
| 700 | 4% | 12 years | 437.217934706045639 |
| 700 | 4.5% | 10 years | 450.749377421030090 |
| 700 | 4.5% | 11 years | 431.339117149311107 |
| 700 | 4.5% | 12 years | 412.764705406039411 |
| 700 | 5% | 10 years | 429.739277478531392 |
| 700 | 5% | 11 years | 409.275502360506096 |
| 700 | 5% | 12 years | 389.786192724291482 |
| 750 | 3% | 10 years | 558.070436172543737 |
| 750 | 3% | 11 years | 541.815957449071561 |
| 750 | 3% | 12 years | 526.034910144729679 |
| 750 | 3.5% | 10 years | 531.689110282329125 |
| 750 | 3.5% | 11 years | 513.709285296936400 |
| 750 | 3.5% | 12 years | 496.337473716846716 |
| 750 | 4% | 10 years | 506.673126619348977 |
| 750 | 4% | 11 years | 487.185698672450940 |
| 750 | 4% | 12 years | 468.447787185048924 |
| 750 | 4.5% | 10 years | 482.945761522532280 |
| 750 | 4.5% | 11 years | 462.149054088547587 |
| 750 | 4.5% | 12 years | 442.247898649327908 |
| 750 | 5% | 10 years | 460.434940155569336 |
| 750 | 5% | 11 years | 438.509466814827931 |
| 750 | 5% | 12 years | 417.628063633169404 |
| 800 | 3% | 10 years | 595.275131917380008 |
| 800 | 3% | 11 years | 577.937021279009628 |
| 800 | 3% | 12 years | 561.103904154378256 |
| 800 | 3.5% | 10 years | 567.135050967817733 |
| 800 | 3.5% | 11 years | 547.956570983398819 |
| 800 | 3.5% | 12 years | 529.426638631303149 |
| 800 | 4% | 10 years | 540.451335060638939 |
| 800 | 4% | 11 years | 519.664745250614260 |
| 800 | 4% | 12 years | 499.677639664052208 |
| 800 | 4.5% | 10 years | 515.142145624034356 |
| 800 | 4.5% | 11 years | 492.958991027784123 |
| 800 | 4.5% | 12 years | 471.731091892616462 |
| 800 | 5% | 10 years | 491.130602832607337 |
| 800 | 5% | 11 years | 467.743431269149823 |
| 800 | 5% | 12 years | 445.469934542047383 |
| 850 | 3% | 10 years | 632.479827662216167 |
| 850 | 3% | 11 years | 614.058085108947807 |
| 850 | 3% | 12 years | 596.172898164026947 |
| 850 | 3.5% | 10 years | 602.580991653306342 |
| 850 | 3.5% | 11 years | 582.203856669861239 |
| 850 | 3.5% | 12 years | 562.515803545759582 |
| 850 | 4% | 10 years | 574.229543501928902 |
| 850 | 4% | 11 years | 552.143791828777694 |
| 850 | 4% | 12 years | 530.907492143055492 |
| 850 | 4.5% | 10 years | 547.338529725536546 |
| 850 | 4.5% | 11 years | 523.768927967020659 |
| 850 | 4.5% | 12 years | 501.214285135904959 |
| 850 | 5% | 10 years | 521.826265509645282 |
| 850 | 5% | 11 years | 496.977395723471659 |
| 850 | 5% | 12 years | 473.311805450925362 |
| 900 | 3% | 10 years | 669.684523407052438 |
| 900 | 3% | 11 years | 650.179148938885874 |
| 900 | 3% | 12 years | 631.241892173675637 |
| 900 | 3.5% | 10 years | 638.026932338794950 |
| 900 | 3.5% | 11 years | 616.451142356323658 |
| 900 | 3.5% | 12 years | 595.604968460216128 |
| 900 | 4% | 10 years | 608.007751943218750 |
| 900 | 4% | 11 years | 584.622838406941128 |
| 900 | 4% | 12 years | 562.137344622058663 |
| 900 | 4.5% | 10 years | 579.534913827038736 |
| 900 | 4.5% | 11 years | 554.578864906257081 |
| 900 | 4.5% | 12 years | 530.697478379193512 |
| 900 | 5% | 10 years | 552.521928186683226 |
| 900 | 5% | 11 years | 526.211360177793495 |
| 900 | 5% | 12 years | 501.153676359803285 |