# Swap Rate vs Par Rate

If we calculate the par rate for n periods, why does the nth swap rate equal the par rate? A mathematical formulation would be helpful apart from an intuitive answer.

Edit: Example:- A 2 year bond pays semiannual coupons and has a par value of $100. Swap Rates- 0.65% (0.5year), 0.8% (1year), 1.02% (1.5 years), 1.16% (2years). Computing discount rates from this gives- 0.9968, 0.9920, 0.9848, 0.977 respectively. Now the par rate would be -$Par/2 * [(d(0.5)+d(1.0)+d(1.5)+d(1.5)+d(2.0)] + 100 * d(2.0) = 100\$

Gives par = 1.16%

• It is not clear what you are asking. Where do you get the conclusion that the nth swap rate equal the par rate? You may see it somewhere, but it is usually related to certain background explained in detail. – Gordon Oct 21 '15 at 15:40
• @Gordon I've added the missing information. Should this be enough? – Piyush Shandilya Oct 21 '15 at 17:34