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. Andreottis shoulders.

Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was demanding an initial down payment of 1.000.000. The total price of the apartment was still not clear, it seems there was some space for negotiation. 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. Mr. Andreotti is fixing the maximum amount he can pay monthly in 2.000.

1) 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. Having said that he wonders what the future value of the rental contract could be. Can you help him? Explain your answer and show your calculations.

2) We are still thinking that the price of the apartment is very expensive, 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%, how much money have we saved with this action?

a) In the payments for each year? b) in the total amount paid for the whole period? c) what is the present value of the savings?

3) There is a risk according to Mr. Andreotti that the interests may rise after the first 5 years. If this is the case, and the new interest rate is 5%, just after the first 5 years, how much will then be the monthly payments for the remaining 35 years of mortgage? (Hint the total initial value of the loan is depends of the offered purchase price in point 2). Explain your answer and show your calculations.