The comparative monthly savings point of view is interesting, but in reality homeownership isn’t exactly a short term concept. My motivation for the short term savings comparison of Parts I and II was this: if our monthly costs of homeownership are greater than our monthly costs of renting (*HO > R)* to the point where our monthly savings are higher while we rent than they would be if we bought (*S _{R} > S_{HO}* – which would require that

*P < HO – R*as I learned in Part I, meaning that

*L > Q*R*as I learned in Part II), then the higher monthly savings

*S*that we gain while we rent might allow us to converge on getting a better home (higher value

_{R}*V*) more quickly than if we bought one now, built up equity (from the

*P*of our

*M*payments), and then sold it to upgrade.

Hmmmm… these kinds of statements are easier to write than they are to read, so I’ll relax a constraint and rephrase for good measure:

**The Main Motivational Question:** If our monthly costs of homeownership *HO* are greater than our monthly costs of renting *R*, will we be able to buy a better home sooner if we a) keep paying rent *R* and build up money for our down payment *D _{R}* , or if we b) buy a place now, simultaneously build up equity

*E*and money for a down payment

*D*, and then move?

_{HO}I suppose what this is all really about is determining which scenario actually results in us having the greatest “worth” over time. To keep things simple, I define our worth while we are renting *W _{R}* to be the money we have available for a down payment

*D*(

_{R}*W*) and our worth while we are homeowners

_{R}= D_{R}*W*to be the equity in our home

_{HO}*E*plus the money we have available for a subsequent down payment

*D*(

_{HO}*W*). So, in order to answer the main motivational question, I need to compare the rate of change of our rental worth

_{HO}= E + D_{HO}*dW*to the rate of change of our homeownership worth

_{R }/dT*dW*while

_{HO}/dT*HO*>

*R*. (I’m using capital

*T*for time…

*T*is normally temperature for me, but I’ve already used lowercase

*t*for my tax rate. Woe.) Things are probably going to get a bit heavier from here, so if you’ve made it this far and this question does not interest you… then I understand if you want to go. Maybe I should have told you what it was all going to be about back at the beginning of Part I, but I honestly didn’t really know until I began to think it through.

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