Pregunta de Matemática e suas Tecnologias #01a0e94a

A real estate company launched an advertising campaign to promote the sale of apartments that can be paid for in 100 monthly installments. The amount of the first installment is set at the time of purchase, along with the payment of that first installment. Starting from the second installment, the value is determined by applying a fixed percentage increase to the previous installment's value. As an incentive, the company will cover all installments corresponding to the buyer's birthday month.

A client, whose birthday is in May, decided to purchase one of these apartments through the financing offered by the real estate company, and intends to choose the most suitable month to make the purchase, such that the total sum of their payments is as low as possible.

Which month should this client choose to purchase the apartment?