Ponder this from the back.

Assume a payment of 1.

Principle in the last payment is v.

Principle in the 2nd to last payment is v^2.

Principle in the 3nd to last payment is v^3.

etc.

Interest in the last payment is 1-v.

Interest in the 2nd to last payment is 1-v^2.

Interest in the 3nd to last payment is 1-v^3.

etc.