You are correct: There is a 1-to-1 relationship between Application and Loan. However, every application does not need a corresponding loan. Applications that have not been processed yet and applications that were rejected will not have a loan associated with them.

The Agreement/Loans table is to track which loans are on each agreement. After a person is approved for a loan, you will create a Loan record. You will then create an Agreement record. Lastly, you would create a record in the Agreements/Loans table to show that the new Loan is a part of the new agreement. To combine two agreements, you would create a third agreement and then add two records to the Agreements/Loans table: the Agreement ID(FK) would be the ID of the new agreement for both records and the Loans ID(FK) would be the ID of the loans that need to be moved to the new Agreement.

Please note that one Loan may appear several times in the Agreements/Loans table. This is to keep a history of the Agreements it used to be on. You may want to add a flag to the Agreements/Loans table to show which record is the "current" record for each Loan.

Another solution is to add an Agreements ID (FK) field to the Loans table. To combine two loans into one agreement, simply enter the same Agreement ID into each Loan. While this method is easier to understand and use, you won't have a history of the Agreements the loan used to be on.