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Question 4.P.7: What is the present value of a stream of monthly payments of......

What is the present value of a stream of monthly payments of $500 each over 10 years, if the interest rate is 10% per annum, compounded monthly?

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Equation (2.7), with the appropriate substitutions, gives

A/P  =  \frac{i(1  +  i)^n}{(1  +  i)^n  –  1}  =  \frac{i}{1  –  (1  +  i)^{-n}}    (3.6) \\\\ P  =  \$500\frac{(1  +  0.10/12)^{(12)(10)  –  1}}{(0.10/12)(1  +  0.10/12)^{(12)(10)}}  =  \$500\frac{1.70704}{(0.0083333)(2.70704)}  =  \$37  835.72

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