# of payments due per month

Counting how many...

You make "Loan 1" with a set # months (the term). Let's say each "Loan 1" has 4 payments (interest only, but irrelevant here): you originate in Month1, and receive payments in Month2 - Month5, and the loan balloons/paid off in Month5. Each month you make a variable number of these loans, but each loan has the same terms. In Month1 you make 2 loan, 3 in Month3, 1 in Month6, 6 in Month9, etc... For each Month1 through Month(n), you want to know how many payments are due.

My real world application is that there are 16 different loan programs with different sets of terms, and I'm calculating the income stream from each loan program. I will also need to count the number of "Loan 1" maturing any given month to calculate the amount of principal returned and available to be loaned back out.

How do I calculate the # of payments due in any given month, given the number of loans made, the month the loan is made, and the length (in months) of each loan?
How do I calculate the # of loans maturing in any given month, given the same data?

Sample attached. Thanks in advance!