The Marco familycomprising Mrs. Marco aged 40, Mr. Marco, aged 39, and their three young children relocated to Barcelona in January 2020 when Mrs. Marco received a job offer from an international firm. They rented a three-bedroom condominium in Barcelona for 2.150 per month, which included parking and fees.

While renting made life easy, the Marco family began weighing the pros and cons of purchasing a flat, in the same building, that became available in June 2020. The idea of home ownership as a form of long-term investment appealed to the couple. The preliminary rental payments could be used for mortgage payments instead.

While searching for the right property they found a nice apartment at one of the best locations of the city. The apartment was owned and had been promoted by a state-owned construction company and was offering two alternatives:

Option I: renting the apartment with a perpetual contract, meaning forever.

The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1,450 EUR the first month, and the rent price will be growing by a 0.15% monthly. This option would prevent the Marco family from applying for a loan, which represented a heavy burden off the family budget.

Option II: consisted in acquiring the property with a mortgage scheme for 30 years. The total price of the apartment is 850.000. The family can pay an initial down payment of 250,000 EUR and the rest (600,000 EUR) to be paid in constant monthly payments with an annual interest rate of a 2.75% compounded monthly.

Mrs. Marco establishes the maximum amount they can pay monthly as 2.250.

• - Mrs. Marco believes that, if she takes option II and acquires the flat, she might be interested in selling the apartment in 30 years time. If she wants to recover all the money invested (initial payments plus all monthly payments done), what will be the price she will ask for that apartment at that moment?
• - Mrs. Marco is happy for knowing how to calculate future values and present values, because this helps in taking financial decisions. She wonders what the future value of the flat will be in 30 years, if the interest rate for this type of operations is an annual 2% (comp. monthly). Find the Future Value of that apartment in 30 years.
• - The Marco family thinks that the monthly payments theyll have to afford during the next thirty years are too much, and believes the seller could be convinced about making constant payments only once per year, at the end of each year. The interest rate would still be the same 2.75% (but now that would be compounded yearly instead of monthly). What is the amount of the yearly payment to be done?
• - In this case (yearly payments) what is the total amount the Marco family will have paid in total after 30 years? (again, just find how much has Mrs. Marco paid in total)
• - In this case (yearly payments), how much has the family saved (if any) by paying yearly instead of monthly installments?
• - In case that the Marco family pays the pending amount in yearly payments, the owner can only grant them 2.75% interest during the first 10 years.

There is the possibility that, after the first 10 years the interest rate increases to a 3.25% for the remaining 20 years. How much should the Marco family pay per year from year 11 onwards if this occurs?