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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 was 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 in 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 forever 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 0.1% monthly. At the same time, they were not forced to ask for a loan, which represented a heavyweight in Mr. Andreotti s shoulders.

Option B:

Consisted in acquiring the property with a mortgage scheme for 40 years, Mr Andreotti would make calculation to 2000 a month, which is the monthly maximum amount he can pay monthly. The ownership was also demanding an initial down payment 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 is the present value of the rental contract offered by the owner as option A?

2) What is the total amount that Mr. Andreotti will pay in total after 40 years in option B?

3) So what is the best option for Mr. Andreotti then? Show the calculations and explain why.

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