Notice 420 months not 360

The Marco family comprising 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 2.100 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 1,650 EUR the first month, and the rent price will be growing by a 0.125% 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 35 years. The total price of the apartment is 875.000. The family can pay an initial down payment of 275,000 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.

In case of taking option I, what is the amount of the monthly payment the Marco family should pay in 35 years (in month 420)? (only the amount to be paid that month, show the calculations)

In case of taking option I, how much money will have the Marco family paid in total after 35 years?

If the Marcon family decides to leave Barcelona in 10 years, to attend a better offer elsewhere, what is the present value of the rental contract offered by the owner as option I? (consider 2.75% compounded monthly as the interest/discount rate)

If Mrs. Marco decides to buy the apartment, and accepts Option II, what will be the amount of each monthly payment to be done during the next 35 years?

Mrs. Marco believes that, if she takes option II and acquires the flat, she might be interested in selling the apartment in 35 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 35 years, if the interest rate for this type of operations is an annual 1.75% (comp. monthly). Find the Future Value of that apartment in 35 years.

The Marco family thinks that the monthly payments theyll have to afford during the next thirty five 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 35 years? (again, just find how much has Mrs. Marconi 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 25 years. How much should the Marco family pay per year from year 11 onwards if this occurs?