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El Cerebro

Mortgage and housing

Renting or buying a home

Two net worth columns for the same person, and what sits between them. Everything is counted with the numbers you type, not with those from a brochure.

What it does

It starts from a home with a given price, down payment and purchase costs, and places two people in the same situation. One buys with a mortgage and the other rents, investing the same amount that the first one puts down. Month by month, each one pays what comes due: payment, owner costs or rent. Whoever spends less invests the difference. At the end of the horizon the account subtracts one net worth from the other and shows the two columns separately, along with the year in which buying moves ahead of renting, if it ever does.

Key concepts

  • Net worth, not money spent: the comparison does not add up what is paid each month, but what is left at the end: the house minus what is owed, plus what was invested. It is the difference between looking at the expense and looking at the result, and only the second one answers the question.
  • Whoever spends less invests the difference: each month, the cheaper of the two puts the money the other has not spent into something that appreciates. Without this rule the comparison would depend on the calendar rather than on the numbers.
  • Same down payment for both: the buyer puts up the down payment and the costs, and the tenant invests that same amount. Both start from the same place, so the difference seen later comes from the two decisions and not from one of them having started out with the whole house.
  • Owner costs: maintenance, insurance, the community fee and the IBI are grouped into an annual percentage of the price that is spread over twelve months. It is a simplification: a specific repair expense is not like a constant one per cent.
  • Appreciation: how much the house is assumed to rise each year. It is the assumption that weighs most heavily on the result and the one nobody knows. With appreciation at 0, the house is an asset that produces nothing on its own.
  • Return on what is invested: what the money the cheaper option did not spend on the house earns. When renting, almost all of the combined capital is invested; when buying, almost all of it is in bricks and mortar.

Frequently asked questions

What difference does this calculator measure?

The net worth of buying minus the net worth of renting at the end of the horizon, in euros. It is the subtraction of two columns that have been filling up with assumptions written by whoever opens the page, not a forecast and not a tax calculation. If it comes out negative, buying comes out behind over those years, and the sign stays as it is: changing it so that the large figure came out positive would be giving the page an opinion it does not have.

Why do the house and the rent change once a year?

That is how contracts work: the rent is reviewed every twelve months and the value of a property is reviewed on the appraiser's date. Applying the same percentage monthly would multiply the house by 1,27 in ten years at 2 % a year, and that figure is invented by the calculator, not by the assumption.

What happens if the mortgage ends before the horizon?

The payment goes to 0 and the debt ends at exactly zero by the end of the term. From then on the owner only pays the owner costs, and the owner is the one who invests the difference against the rent, which no longer competes with any payment. The series shows it: the point in the year when the loan ends is the first one in which the house belongs entirely to the owner.

What happens with an interest rate of zero per cent?

The closed formula turns into a division by zero. Its limit is the amount split into equal parts: 60.000 € over ten years gives 500 € a month, with not one euro of interest. That is the case of a family loan and of the valuation, not a typing error.

What limits do the fields accept?

The price runs from 10.000 to 5.000.000 €, the percentages for costs, down payment, rate, appreciation and return all have their own caps, and the horizon runs from 1 to 40 years. An empty field does not equal zero: leaving it blank and typing 0 are two different intentions. If the down payment and the purchase costs add up to more than 100 % of the price, the calculator warns you instead of calculating a negative mortgage.

What does this calculator NOT cover?

Neither taxes, nor selling costs, nor deductions, nor default risk, nor any market data. The ITP or the IVA on the purchase, the IRPF on the invested amount, the capital gains tax on a sale, the cost of a change of tenant and the risk premium on a default are all left out. They are eleven assumptions and a subtraction: what is not in the account is here in the text, not hidden inside a number.

Does the account round the results?

No. The calculation keeps all of its decimals and the rounding happens when the figures are presented, the same as in the rest of the site's calculators. Intermediate rounding would give prettier and false amounts: in a series of fifteen points, a cent of difference shows.

Is the figure a recommendation?

No. It is the difference between two columns built with the numbers of whoever opens the page. Both outcomes are equally legitimate and depend on assumptions that only that person knows: their horizon, their tolerance for uncertainty and what they intend to do with the money. The decision belongs to whoever is reading.

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