The repayment instalment of a fixed rate, fixed period loan may be calculated by summing the present

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The repayment instalment of a fixed rate, fixed period loan may be calculated by summing the present values of each instalment. This sum must equal the amount borrowed. The present value of an instalment £x paid after k years where r% is the rate of interest is

(1 + r/100)*

Thus £1000 borrowed over n years at r% satisfies the equation

1000 = - + 1 + r/100 (1 + r/100) + X X (1 + r/100)

Find x in terms of r and n and compute its value when r = 10 and n = 20.

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