The Andreotti familycomprising Mr. Andreotti, aged 40, Mrs. Andreotti, aged 38, and their three young children relocated to Barcelona in 2020 when Mr. Andreotti received a job offer from a leading investment banking giant. For the next six years, they rented a three-bedroom condominium for 2.000 in Barcelona per month, which included parking and condominium fees.

While renting made life easy, the Andreotti family began weighing the pros and cons of purchasing a flat, in the same building, that became available in June 2020. In the past three years, the real estate market had softened somewhat, and the cost of the flats were stable. The idea of home ownership as a form of pension investment appealed to the couple. The monthly rents could be used for mortgage payments instead.

While searching for the right property they found a nice apartment with 200 square meters, very close to Diagonal-Numancia, one of the best locations of the city.

The apartment was owned and been promoted by a state-owned construction company and was offering to type of alternatives:

Option A: Renting the apartment with a perpetual contract, meaning for ever and ever. The Andreotti family thought that could be a good solution for them. The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1.600 per month. The contract contained a clause stating that the rent price will be growing at a 0.1% monthly. At the same time, they were not forced to ask for a loan, which represented a heavy weight in Mr. Andreotti s shoulders.

Option B: Consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was also demanding an initial downpayment of 1.000.000 in this case. Mr. Andreotti new that the interest applicable rates were very attractive, around 2.4% compounded monthly, this is supposed to be the market rate for this type of activities.

1) What would be the best option between A and B for Mr. Andreotti, if he considers maximum a 2.000 monthly payment according to his earnings? Show the calculations and explain why.

2) What is the present value of the rental contract offered by the owner as option A?

3) What is the monthly fee that Mr. Andreotti will have to pay after 40 years in option B, if he finally negotiates a price reduction to 1.450.000? He still will have to make the down payment of 1.000.000.

4) Mr. Andreotti believes that he might be interested in selling the apartment in 40 years time (option B), this is when he is planning to retire. With that amount sold, he may be able to retire. So he will be receiving from the Bank a monthly payment for his retirement. How much will he earn if he lives 25 years?

5) Mr. Andreotti is very happy for knowing how to calculate future values and present values, because this helps him in taking this type of decisions and to know the savings of each option. What is the equivalent value of the perpetual contract in year 40 to allow him to compare with option B? Explain your answer and opinion according to the data and calculations done. What are the pros and cons of renting or buying a house then?

6) We are still thinking that the price of the apartment is very expensive (option B), we believe we could convince the bank of making payments only once a year, at the end of the year. The interest rate would still be the same 2.4% annually and the payment accumulated to the end of the year, with this action?

a) How much money would Mr.Andreotti save in the yearly payments (at a 2,4 interest rate compounded yearly) compare to monthly payments (at a 2,4% compounded monthly)?

b) How much money would Mr.Andreotti save in total after 40 years? Discount the two options at present to calculate the total saving.

7) After 5 years at a 2,4% rate compounded monthly, Mr. Andreotti experience a rise of interest rates. What is the value of the option B today, if the new interest rate from year 5 is 7% compounded monthly?