Design pattern for many-to-many association with additional fields and partial satisfaction

I am working on a project in which customers can get loans, that will be divided in n instalments.

The customer will make payments.

class Instalment
  has_and_belongs_to_many :payments
end

class Payment
  has_and_belongs_to_many :instalments
end

He can pay the whole loan or a single instalment, but the idea is that he can pay any kind of quantity.

This means that some instalments will be partial paid.

I am not sure about how to express this in the code.

E.g., The customer get a loan of 50$, which will be divided in 5 instalments of 10$. The customer decides to pay 25$ two times.

Instalment
--------------
ID | quantity
 1 |      10$
 2 |      10$
 3 |      10$
 4 |      10$
 5 |      10$

Payment 
----------------------
ID | quantity
 1 |      25$
 2 |      25$

Instalments_Payments 
----------------------
payment_id | instalment_id
         1 |             1
         1 |             2
         1 |             3    # note that this instalment_id and next one
         2 |             3    # are the same, but we don't know how much quantity it satisfied in each one.
         2 |             4
         2 |             5

I have two ideas, but I don't like any of them:

Add a two new field in the Instalments_Payments table. One will tag if the instalment has been totally paid and the other how much it was paid.

Instalments_Payments 
----------------------
payment_id | instalment_id | full_paid | paid
         1 |             1 |      true |  10$ 
         1 |             2 |      true |  10$
         1 |             3 |     false |   5$
         2 |             3 |     false |   5$
         2 |             4 |      true |  10$
         2 |             5 |      true |  10$

Add a new model PartialPayments in which a payment has_many :partial_payments

I am looking for the best approach of this issue.