Calculation of interest on balance due - sql-server-2017

Question

I have 3 tables Invoice, Payments and InterestRate. For purposes of simplicity I am representing each of the tables as follows.
The Invoice table has the following columns (the InvNum is the primary key)
+--------------+-------------+---------------+
| InvNum | InvDate | InvAmt |
+--------------+-------------+---------------+
| 123 | 2017-03-09| 15000 |
| 456 | 2017-01-13| 20000 |
+--------------+-------------+---------------+
The Payment table is as follows (the InvNum in the payments table is a foreign key which links to the Invoice table above
+--------------+------------+----------+
| payment_date | InvNum | amount |
+--------------+------------+----------+
| 2017-08-10 | 123 | 5000 |
| 2017-08-15 | 456 | 3000 |
| 2017-09-15 | 123 | 3000 |
| 2017-10-11 | 456 | 4000 |
| 2017-10-16 | 123 | 3500 |
| 2017-11-10 | 123 | 3000 |
| 2017-11-15 | 456 | 2500 |
+--------------+------------+----------+
My InterestRate looks something like this
+--------------+-------+
| ResetDate | IntRate|
+--------------+--------+
| 2016-01-01| 10 |
| 2017-06-08| 10.25 |
| 2017-11-03| 10.67 |
| 2018-05-03| 10.83 |
| 2018-07-29| 10.72 |
| 2019-01-01| 10.67 |
+------------+----------+
What I need is to calculate the interest for each Invoice after considering each payment and the final balance due on the invoice (in case it has not been fully paid). The final table should look something like this
InvNum IntFrom IntTo Amount IntRate Interest Payment Balance
123 2017-03-09 2017-06-07 15000 10 xxx 0 15000
123 2017-06-08 2017-08-10 15000 10.25 yyy 5000 10000
123 2017-08-11 2017-09-15 10000 10.25 zzz 3000 7000
123 2017-09-16 2017-10-16 7000 10.25 aaa 3500 3500
123 2017-10-17 2017-11-02 3500 10.67 bbb 0 3500
123 2017-11-03 2017-11-15 3500 10.67 ccc 2500 1000
123 2017-11-16 2018-05-02 1000 10.67 ddd 0 1000
123 2018-05-03 2018-07-28 1000 10.83 eee 0 1000
123 2018-07-29 2018-12-31 1000 10.72 fff 0 1000
123 2019-01-01 (today) 1000 10.67 ggg 0 1000
I have not shown the results of Inv#456. But the desired solution needs to group each of the invoices in the invoice table.
So in effect the interest calculation takes into account the payments made against each invoice (listed in the Payments table) as well as the changing interest rates (listed in the InterestRate table). Of equal importance is the fact that the interest on the balance due on each invoice (1000 for inv#123) needs to calculated till the date of running the query.
One of the challenges I am also facing is how can I capture the above results in a table. Would it mean dropping and recreating the table every time you run the query (since everytime the date changes the interest amount on the balance due will undergo a change). So unless only the interest on the balance per invoice can be updated, it would (should?) necessarily mean that the table has to be dropped and re-created. Alternatively, the results have to be viewed through a view query.
I hope I have been able to articulate my problem satisfactorily.
Thanks a lot for your time and attention to helping me out