As it stands, this doesn't literally make sense. It must refer to some kind of monthly premium that X (clearly the insured) has to pay: "se obliga a pagar a la aseguradora". It is calculated as a proportion of the sum insured ("los saldos reportados por el asegurado"). In that case, if 3.586% is really a percentage, "al millar" is redundant: if the premium referred to is 3.586 per cent of the sum, 3.586% per thousand of the sum is the same thing; the rate is paid on however much it is.

In any case, this rate is implausible. 3.586% per month would be extremely high.

I think "% al millar" is being used here to mean simply "per thousand", which can be expressed as "per mille", or by the symbol "‰". Maybe the symbol was not available.

So what it means is 3.586 per mille (3.586‰) per month of the "suma de los saldos reportados). This would be equivalent to 0.3586%.

Some supporting evidence: first, as mentioned, this is a plausible rate. Here is a legal provision from Mexico on the "cuota mensual que deberán pagar por concepto del Seguro de Depósitos las Sociedades Cooperativas de Ahorro y Préstamo":

"pagarán por concepto del Seguro de Depósitos al Fondo de Protección cuotas ordinarias por un monto equivalente a la duodécima parte de 3 al millar sobre los saldos al último día del mes de sus depósitos de dinero del segundo mes inmediato anterior"
http://dof.vlex.com.mx/vid/aviso-ref-328392-285898139

The "duodécima parte" refers, of course, to the fact that it quoted as monthly rather than yearly.

Second, an example of "porcentaje al millar" used to mean simply "per mille", or per thousand:

"propongo que se pague un porcentaje al millar, a manera de ejemplo: por cada mil pesos del valor de la propiedad sería pagar un peso: si tienes una propiedad de cien mil pesos pagarás 100 pesos y si tu propiedad vale quinientos mil, pagarás quinientos pesos, según se defina el porcentaje"
http://www.manzanillo.tv/0612/09/felipe.html

And "per thousand" rates in insurance generally are not that unusual.