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Question
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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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography