Solving for VariableDate: 2/7/96 at 22:19:14 From: Anonymous Subject: Solving for Variable If; Pt = PV(R) / (1-(1+R)EXP(-N)) is used to determine a Pt (monthly payment), if PV (present value), R (rate) and N (term) are known, how is this simplified to solve for R? Date: 7/22/96 at 22:16:2 From: Doctor Jerry Subject: Re: Solving for Variable I'd like to change your notation a little. Let P stand for Pt, V for PV, and leave the remaining variables the same. Your equation is (I think) P=V*R/(1-(1+R)e^(-N)). Start by multiplying both sides of this equation by (1-(1+R)e^(-N)). This gives P*(1-(1+R)e^(-N))=V*R. Expand the left side to get P-P*e^(-N)-P*R*e^(-N)=V*R. Move all terms involving R to the left and all other terms to the right. -V*R-P*R*e^(-N)=-P+P*e^(-N). Factor R from the two terms on the left and change some signs R(V+P*e^(-N))=P(1-e^(-N)). Finally, R=P(1-e^(-N))/(V+P*e^(-N)) or, multiplying top and bottom of the fraction on the right by e^N, R=P(e^N-1)/(V*e^N-P). I hope this is clear. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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