Off market swap with swap premium


I am new to the forum and i am struggling to understand the valuation of an off market interest rate swap with an upfront payment.

I understand that the upfront payment is driven by the present value that the fixed rate of my off market interest rate is different that if i have an on market swap, hence i would either receive or pay a payment to compensate this fact.

However, i don’t understand how the valuation of this derivatives would drive back to the notional at the end of its life, if each subsequent un-discounted cash flows are still based on the off market swap terms. How would my upfront swap premium balance deplete back to 0?

Confused. :sob:

Appreciate if someone can shed some light.