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. crying 

Appreciate if someone can shed some light.