Math Problems: Renting vs. Buying

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We want to buy a house so we have roots, and so our home improvements are not a waste, and we broke it down over the life of the mortgage to see if it makes sense. In Guatemala, you have to know that you are essentially throwing your money to the winds and you might NEVER see your house sell, or there could be an earthquake (no insurance), or the water could rise over your house. So, we started really breaking it down: See below.
Current State: Our rent is $600 and with that comes an empty shell of a house. In order to make it comfortable (at a minimum), we need to accumulate, build and develop. Yay, projects. Kurt and I are project people. That might be our biggest issue, but we certainly have fun with it and look at everything as a learning experience. Sadly, I suppose one thing that we do (always) is excuse ourselves from reality and just allow ourselves with the freedom to dream and execute fully.  Most people do not do this and I am often given shit about it from everyone in my life.
The Rationalization: Regarding the improvements, if you really look into what anyone would spend, anywhere, you will never get compensated for the kinds of improvements we are making, Kurt’s studio is costing us a whopping $1,800 and it is a custom built studio space which he would have to do even if he rented a studio in Harlem (and there it would be $8,000 to do what we are doing here and it would still be an unusable space for anyone that is not a painter, certainly not adding any value to a resale), a Sauna is $1200, Gardening is maybe $600 tops. We don’t even pay for our 2 full-time gardeners, so we are not putting that many resources into the gardens. I just want it to look better and to have a vegetable and herb garden. We are going to literally eat what we buy. That is two weeks food budget in NYC!
But we have been thinking about buying and what that would entail. Actually we were literally ready to sign on the dotted line here, but the owner was unwilling to sell at the time (different house).
The Breakdown: The asking price is $450,000 for the house we are in. If we are to double our rent with improvements, it would be roughly $15,000 a year, and we could live here for 30 years before we spend the asking price of the house (let alone the cost of 2 full-time gardeners year after year and the cost of on going house improvements… which are getting more expensive with the lake rising). If we live in this house for our actual rent (i.e. without the improvements) we could live here for 62 years. Can you believe it? Our rent per month in NYC is $3k. If we spend roughly double our rent to include our improvements we will still only spend 5 months of rent worth in NYC for the whole year.
The New Possible Plan: After really thinking about it, why do we want to buy? Why shouldn’t we just rent and try to get a 5-10 year lease somewhere? It seems to make a lot of sense to me, considering no one these days ever recoups the energy and money put into a house. And it binds you to a place. We are global family and being nailed down to the ground of a house doesn’t appeal much to either of us. But we don’t have a real home if we don’t buy. And we don’t have roots for our children to come back to.
Back to the Rationalization: So when you break down the improvements that we are making, we are just giving ourselves a little present. Here’s the example: If we use the sauna, like most do a hot tub, we are are looking at a pretty inexpensive gym membership, considering we have the lake for swimming and the hiking for a Stairmaster. Again, in NYC, Iza’s gym was a whopping $125 a month, ours was around $250 for the two of us for the basic package. That is $4,500 a year.
Who know which is the better way with renting vs. buying these days? We certainly don’t and it is a risk either way. I suppose it is my own justification, but there is what everyone calls “The Right Way”: the way to save money and to really spend energy playing it safe and investing in our future. And then there is The Brand Way: always making things more challenging for ourselves and investing in our now. But The Brand Way could mean buying a house…. you just never know.