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Default Conditional Problem Solving

Outstanding Debt (A1) is given
Interest Rate (A2) is given
Period (A3) is given
Interest Payment (A4) is calculated in a formula using the values in A1, A2,
and A3
Principal Payment (A5) IS WHAT I AM TRYING TO SOLVE FOR
Outstanding Debt #2 (B1) is A1 - A5
Interest Payment #2 (B4) is calculated in a formula using the values in B1,
A2 and A3

The problem is that I am trying to find the largest number for A5 with the
following conditions:

A5 must be multiple of 5,000
The sum of A4, A5 and B4 must come as close to 6,172,000 without exceeding
that number.

Any ideas on how I might accomplish this in Excel?
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