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All my records burned this New Year. I hold a note on land. It is being paid off monthly. I know that for the year 2012 the payments were $1200 each month, and the total interest paid for that year was $8687, total principle $5713. The interest rate is 7% per year . What was the principle at the beginning of 2012?

Given an original principal of P0, the formula for remaining principal after N payments is given by

P(N) = P0(1+r)^N - a[(1+r)^N - 1]/r

where r = interest per payment period and a = amount paid per period. We want to solve for P0. We know that over a year (N = 12 = payments), the principal has gone down by

∆P = P(N) - P0

so that

P0 = {∆P + a[(1+r)^N - 1]/r}/[(1+r)^N-1]

We have that

∆P = 5713

r = 0.07/12 = 0.00583 (monthly interest rate)

a = 1200.

Plugging these in gives P0 = 285,889.

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