Incomplete

Back to the incomplete information issue for our loan repayment app.:
We want to see if we can reconstruct the loan amount from interest paid over  one
year and amount of payment. Let us create a simple situation of 100$  at 5% yearly repaid
in full over one year. Using our formula for payment:

p = .00417 * 100/(1 - (1/1.00417)^12)
 = 8.57$
Multiplying by 12 we got, 102.81$

Can we reconstruct  the loan payment, knowing we paid 2.81$ interest over one year. Of course; we merely solve for, in the above formula:
(p * 12) - 2.81 = PV

Now let's make things more complicated. We'll be working with a 200$ loan, at 5%, over two
years.Total repayment here totals 210.69$ with 10.69 interest. Alas, the bank sends us an enigmatic
tax paper to the effect that we have paid 5.32$ in interest last year. Looking at the amortization
schedule, this amount is the interest from the last six months of the first year and the first six of
the second.

Clearly, we are going to need more information...