S_Loan(Part2)

Moving on to the next utility in our Student Loan application. Let us say that
I receive a paper from the Bank, informing me that I have paid x amount in
interest on a loan in the taxation year; I remember that the interest rate
was 3% but little else. Can one reconstruct the rest of the situation.

As described, no. One can build scenarios that range from complete repayment, to payment of interest only, and many in-between. One needs one or more parameter: payment amount,
initial amount due, or end-of-the-year amount due. Here is the relevant formula.

P = r*(PV)/(1 - (1 + r)^-n)

monthly payment = rate*(initial amount)/(1-(1 + rate)^-(no of payments))

This formula would define, for a 1000$ loan at 5%, a monthly payment of
85.56$. Multiplied by 12, for a total of 1026.77$. The loan would have cost
26.77$. Here the transaction is complete after one year.

Had I remembered that I was making 50$ per month payments, use of the formula
would tell me I had paid 584.35$ in principal and 15.65$ in interest. Because I do
not know when payments will end, I cannot estimate the other parameters. I need
either beginning amount, or end-of-year amount to find the missing one.

I can create an app page for this situation.