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Finance algebra 
With the following variables the periodic (annual) repayment is given by The recurrence equation for the balance b at the end of month x is derived from b[x + 1] = b[x] (1 + r) - d where b[0] = s giving The interest portion of the final payment is b[n - 1] r and the total principal repaid at the end of period n - 1 is s - b[n - 1] Solving simultaneously n = 8.9998 and s = 7240 The principal repaid at the end of the first period is s - b[1] or d - r s = 479.74